Skip to main content Accessibility help
×
Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-25T17:42:41.213Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  06 December 2019

Nikolaï Nikolski
Affiliation:
Université de Bordeaux
Get access
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Primary Sources

Acosta, G. and Durán, R. (2004), An optimal Poincaré inequality in L1 for convex domains. Proc. Amer. Math. Soc. 132:1, 195–202.Google Scholar
Adams, D. R. and Hedberg, L. I. (1996), Function Spaces and Potential Theory. Springer.CrossRefGoogle Scholar
Adamyan, V. M., Arov, D. Z., and Krein, M. G. (1968), On infinite Hankel matrices and the generalized problems of Carathéodory–Fejér and Riesz, F. (in Russian). Funkcional. Analiz i Prilozhen. 2, 1–19. English translation: Funct. Anal. Appl. 2, 1–18.Google Scholar
Adamyan, V. M., Arov, D. Z., and Krein, M. G. (1971), Infinite Hankel block matrices and some related continuation problems (in Russian). Izvestia Akad. Nauk Armyan. SSR Ser. Mat. 6, 87–112. English translation: Amer. Math. Soc. Transl. (II) 111 (1978), 133–156.Google Scholar
Akhiezer, N. I. (1965), Lectures on Approximation Theory (in Russian), second edition. Nauka, Moscow. English translation: Approximation Theory, Dover, New York (1992).Google Scholar
Akhiezer, N. I. and Krein, M. G. (1938), Some Questions in the Theory of Moments (in Russian). GONTI, Kharkov. English translation: vol. 2 of Translations of Mathematical Monographs, American Mathematical Society, Providence, RI (1962).CrossRefGoogle Scholar
Aleman, A., Pott, S., and Reguera, M. C. (2013), Sarason conjecture on the Bergman space. arXiv:1304.1750v1Google Scholar
Aleman, A. and Vukotic, D. (2009), Zero products of Toeplitz operators. Duke Math. J. 148:3, 373–403.Google Scholar
Allan, G. R. (1968), Ideals of vector-valued functions. Proc. London Math. Soc. (3) 18, 193–216.Google Scholar
Alzer, H. (2002), Inequalities for the constants of Landau and Lebesgue. J. Comput. Appl. Math. 139, 215–230.CrossRefGoogle Scholar
Anosov, D. and Bolibruch, A. (1994), The Riemann–Hilbert problem, vol. E22 of Aspects of Mathematics. Vieweg, Braunschweig.Google Scholar
Arcozzi, N., Rochberg, R., Sawyer, E. T., and Wick, B. D. (2010), Bilinear forms on the Dirichlet space. Anal. PDE 3:1, 21–47.Google Scholar
Arcozzi, N., Rochberg, R., Sawyer, E. T., and Wick, B. D. (2011), The Dirichlet space: a survey. New York J. Math. 17, 45–86.Google Scholar
Aronszajn, N. (1950), Theory of reproducing kernels. Trans. Amer. Math. Soc. 68, 337–404.Google Scholar
Arsene, G. and Gheondea, A. (1982), Completing matrix contractions. J. Oper. Theory 7, 179–189.Google Scholar
Arveson, W. (1975), Interpolation problems in nest algebras. J. Funct. Anal. 20:3, 208–233.Google Scholar
Atiyah, M. and Singer, I. (1963), The index of elliptic operators on compact manifolds. Bull. Amer. Math. Soc. 69:3, 322–433.Google Scholar
Atkinson, F. V. (1951), Normal solvability of linear equations on normed spaces (in Russian). Mat. Sbornik 28:1, 3–14.Google Scholar
Axler, S., A. S.-Y. Chang, and Sarason, D. (1978), Products of Toeplitz operators. Integral Equations Oper. Theory 1, 285–309.Google Scholar

Secondary Sources

Bakonyi, M. and Timotin, D. (2001), On an extension problem for polynomials. Bull. London Math. Soc. 33, 599–605.Google Scholar
Bakonyi, M. and Woerdeman, H. (2011), Matrix Completion, Moments, and Sums of Hermitian Squares. Princeton University Press.Google Scholar
Banach, S. (1932), Théorie des opérations linéaires. Monografje Matematyczne, Warsaw.Google Scholar
Baranov, A., Bessonov, R., and Kapustin, V. (2011), Symbols of truncated Toeplitz operators. J. Funct. Anal. 261:12, 3437–3456.CrossRefGoogle Scholar
Barria, J. and Halmos, P. (1982), Asymptotic Toeplitz operators. Trans. Amer. Math. Soc. 273:2, 621–630.Google Scholar
Bart, H., Hempfling, T., and Kaashoek, M. A., eds (2008), Israel Gohberg and Friends: On the Occasion of his 80th Birthday. Birkhäuser, Basel and Boston.Google Scholar
Baxter, G. (1963), A norm inequality for a “finite section” Wiener–Hopf equation. Illinois J. Math. 7, 97–103.Google Scholar
Baxter, G. and Hirshman, I. I. (1964), An explicit inversion formula for finite-section Wiener–Hopf operators. Bull. Amer. Math. Soc. 70, 820–823.Google Scholar
Beckenbach, E. F. and Bellman, R. (1961), Inequalities. Springer.Google Scholar
Bercovici, H., Foias, C., and Tannenbaum, A. (1988), On skew Toeplitz operators, I. In vol. 29 of Operator Theory: Advances and Applications, pp. 21–45. Birkhäuser, Basel.CrossRefGoogle Scholar
Bercovici, H., Foias, C., and Tannenbaum, A. (1998), On skew Toeplitz operators, II. In vol. 104 of Operator Theory: Advances and Applications, pp. 23–35. Birkhäuser, Basel.CrossRefGoogle Scholar
Berezin, F. A. (1972), Covariant and contravariant symbols of operators (in Russian). Izvestia Akad. Nauk. SSSR Ser. Mat. 36, 1134–1167.Google Scholar
Berezin, F. A. (1989), The Method of Second Quantization, revised (augmented) second edition. Kluwer. First English edition: Academic Press (1966).Google Scholar
Berg, C., Christensen, J., and Ressel, P. (1984), Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions. Springer, New York.Google Scholar
Berger, C. A. and Shaw, B. I. (1973), Intertwining, analytic structure, and the trace norm estimate. In Proc. Conf. on Operator Theory (Halifax, 1973), vol. 345 of Lecture Notes in Mathematics, pp. 1–6. Springer, Berlin and Heidelberg.CrossRefGoogle Scholar
Bertrand, G. (1921), Equations de Fredholm à intégrales principales au sens de Cauchy. CR Acad. Sci. Paris 1972, 1458–1461.Google Scholar
Bessonov, R. V. (2014), Duality theorems for coinvariant subspaces of H1. arXiv:1401.0452v1Google Scholar
Bini, D. (1995), Toeplitz matrices, algorithms and applications. ECRIM News online edition 22, July 1995. www.ercim.eu/publication/Ercim_News/enw22/toeplitz.htmlGoogle Scholar
Birkhoff, G. D. (1909), Singular points of ordinary linear differential equations. Trans. Amer. Math. Soc. 10, 436–470.Google Scholar
Birkhoff, G. D. (1913), The generalized Riemann problem for linear differential equations and the allied problems for linear difference and q-difference equations. Proc. Amer. Acad. Art Sci. 49, 521–568.Google Scholar
Blasco, O. (2004), Remarks on operator BMO spaces. Revista Union Mat. Argentina 45:1, 63–78.Google Scholar
Bleher, P. M. (1979), Inversion of Toeplitz matrices (in Russian). Trudy Moscow Math. Soc. 40, 207–240. English translation: Trans. Moscow Math. Soc. (1981), 201–224.Google Scholar
Bonsall, F. F. (1984), Boundedness of Hankel matrices. J. London Math. Soc. (2) 29, 289–300.Google Scholar
Borodin, A. and Okounkov, A. (2000), A Fredholm determinant formula for Toeplitz determinants. Integral Equations Oper. Theory 37:4, 386–396.Google Scholar
Böttcher, A. (1994), Pseudospectra and singular values of large convolution operators. J. Integral Equations Appl. (6) 3, 267–301.Google Scholar
Böttcher, A. (1995), The Onsager formula, the Fischer–Hartwig conjecture, and their influence on research into Toeplitz operators. J. Statist. Phys. (Lars Onsager Festschrift) 78, 575–584.Google Scholar
Böttcher, A. (2001), Featured review on [43]. Math. Reviews MR1780118 (2001g:47042a).Google Scholar
Böttcher, A. and Grudsky, S. M. (1996), Toeplitz operators with discontinuous symbols: phenomena beyond piecewise continuity. In vol. 90 of Operator Theory: Advances and Applications, pp. 55–118. Birkhäuser, Basel.Google Scholar
Böttcher, A. and Grudsky, S. M. (2005), Spectral Properties of Banded Toeplitz Matrices. SIAM, Philadelphia.Google Scholar
Böttcher, A., Bogoya, J. M., S. M. Grudsky, and Maximenko, E. A. (2017), Asymptotic formulas for the eigenvalues and eigenvectors of Toeplitz matrices (in Russian). Mat. Sbornik 208, 4–28. English translation: Sbornik Math. 208 (2017), 1578–1601.Google Scholar
Böttcher, A. and Karlovich, Y. (1997), Carleson Curves, Muckenhoupt Weights, and Toeplitz Operators, vol. 154 of Progress in Mathematics. Birkhäuser, Basel.Google Scholar
Böttcher, A., Karlovich, Y., and Spitkovsky, I. (2002), Convolution Operators and Factorization of Almost Periodic Matrix Functions, vol. 131 of Operator Theory: Advances and Applications. Birkhäuser, Basel.Google Scholar
Böttcher, A. and Silbermann, B. (1990), Analysis of Toeplitz Operators. Akademie, Berlin, and Springer.Google Scholar
Böttcher, A. and Silbermann, B. (1999), Introduction to Large Truncated Toeplitz Matrices. Springer, New York.Google Scholar
Böttcher, A. and Spitkovsky, I. M. (2013), The Factorization Problem: Some Known Results and Open Questions. In Advances in Harmonic Analysis and Operator Theory (ed. A. Almeida, Castro, L., and F.-O. Speck), vol. 229 of Operator Theory: Advances and Applications, pp. 101–122. Birkhäuser, Basel.Google Scholar
Böttcher, A. and Widom, H. (2006), Szegö via Jacobi. Linear Alg. Appl. 419, 656–667.Google Scholar
Böttcher, A. and Widom, H. (2007), From Toeplitz eigenvalues through Green’s kernels to higher-order Wirtinger–Sobolev inequalities. In vol. 171 of Operator Theory: Advances and Applications, pp. 73–87. Birkhäuser, Basel.Google Scholar
Bourbaki, N. (1967), Eléments de mathématique, book XXXII: Théories spectrales. Hermann, Paris.Google Scholar
Boutet, L. de Monvel and Guillemin, V. (1981), The Spectral Theory of Toeplitz Operators. Princeton University Press.Google Scholar
Brown, L. G., Douglas, R. G., and Fillmore, P. A. (1973), Unitary equivalent modulo the compact operators and extensions of C*-algebras. In Proc. Conf. on Operator Theory (Halifax, 1973), vol. 345 of Lecture Notes in Mathematics, pp. 58–128. Springer, Berlin and Heidelberg.Google Scholar
Brown, A. and Halmos, P. (1963), Algebraic properties of Toeplitz operators. J. Reine Angew. Math. 213, 89–102.Google Scholar
Brown, A., Halmos, P. R. and Shields, A. L. (1965), Cesàro operators. Acta Sci. Math. Szeged 26, 125–137.Google Scholar
Burbea, J. and Masani, P. R. (1984), Banach and Hilbert Spaces of Vector-Valued Functions: Their General Theory and Applications to Holomorphy. Pitman.Google Scholar
Carathéodory, C. (1907), Über den Variabilitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen. Math. Ann. 64, 95–115.Google Scholar
Carathéodory, C. (1911), Über den Variabilitätsbereich der Fourierschen Konstanten von positiven harmonischen Funktionen. Rend. Circ. Mat. Palermo 32, 193–217.Google Scholar
Carathéodory, C. and Fejér, L. (1911), Über den Zuzammenhang der Extremen von harmonischen Funktionen mit ihren Koeffizienten und über den Picard–Landauschen Satz. Rend. Circ. Mat. Palermo 32, 218–239.Google Scholar
Cauchy, A. L. (1841), Exercices d’analyse et de physique mathématique, vol. 2, second edition. Bachelier, Paris.Google Scholar
R. H.-F. Chan and Jin, X.-Q. (2007), An Introduction to Iterative Toeplitz Solvers, vol. 5: Fundamentals of Algorithms. SIAM.Google Scholar
Chandrasekharan, K., ed. (1986), Weyl Centenary Symposium, 1885–1985. Springer.Google Scholar
S.-Y. A. Chang (1976), A characterization of Douglas subalgebras. Acta Math. 137, 81–89.Google Scholar
Chevalley, C. and Weil, A. (1957), Hermann Weyl. Enseignement Math. 3:3, 157–187.Google Scholar
Choi, M.-D. (1983), Tricks or treats with the Hilbert matrix. Amer. Math. Monthly 90:5, 301–312.Google Scholar
Clancey, K. and Gohberg, I. (1981), Factorization of Matrix Functions and Singular Integral Operators, vol. 3 of Operator Theory: Advances and Applications. Birkhäuser, Basel.Google Scholar
Coburn, L. A. (1966), Weyl’s theorem for nonnormal operators. Mich. Math. J. 13, 285–288.Google Scholar
Coburn, L. A. (1967), The C*-algebra generated by an isometry I. Bull. Amer. Math. Soc. 73, 722–726.Google Scholar
Coburn, L. A. (1969), The C*-algebra generated by an isometry II. Trans. Amer. Math. Soc. 137, 211–217.Google Scholar
Coburn, L. and Douglas, R. G. (1969), Translation operators on the half-line. Proc. Nat. Acad. Sci. USA 62, 1010–1013.Google Scholar
Coburn, L. and Lebow, A. (1966), Algebaic theory of Fredholm operators. Indiana Univ. Math. J. 15, 577–584.Google Scholar
Cohen, P. (1961), A note on constructive methods in Banach algebras. Proc. Amer. Math. Soc. 12:1, 159–163.Google Scholar
Coifman, R. R., Rochberg, R., and Weiss, G. (1976), Factorization theorems for Hardy spaces in several variables. Ann. Math. 103, 611–635.Google Scholar
Coifman, R. R. and Weiss, G. (1977), Transference Methods in Analysis, vol. 31 of CBMS Regional Conference Series in Mathematics. American Mathematical Society, Providence, RI.Google Scholar
Colin, Y. de Verdière (1995), Une introduction aux opérateurs de Toeplitz. Séminaire de Théorie spectrale et géométrie 13, 135–141.Google Scholar
Cordes, H. O. and Labrousse, J. P. (1963), The invariance of the index in the metric space of closed operators. J. Math. Mech. 12, 693–719.Google Scholar
Cotlar, M. and Sadosky, C. (1979), On the Helson–Szegö theorem and related class of modified Toeplitz kernels. In Harmonic Analysis in Euclidean Spaces (Williamstown, MA, 1978), part 1 (ed. G. Weiss and S. Wainger), vol. 35 of Proceedings of Symposia in Pure Mathematics, pp. 387–407. American Mathematical Society, Providence, RI.Google Scholar
Courant, R., Friedrichs, K., and Lewy, H. (1928), Über die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann. 100, 32–74.Google Scholar
Crofoot, R. B. (1994), Multipliers between invariant subspaces of the backward shift. Pacific J. Math. 166:2, 225–246.Google Scholar
Davidson, K. (1988), Nest Algebras, vol. 191 of Pitman Research Notes Series. Longman Scientific & Technical.Google Scholar
Davis, P. J. (1994), Circulant Matrices. Chelsea Publishing, New York.Google Scholar
Deift, P. (2000), Orthogonal Polynomials and Random Matrices: A Riemann–Hilbert Approach, Courant Lecture Notes. American Mathematical Society.Google Scholar
Deift, P., Its, A., and Krasovsky, I. (2013), Toeplitz matrices and Toeplitz determinants under the impetus of the Ising model: some history and some recent results. Comm. Pure Appl. Math. 66:9, 1360–1438.Google Scholar
Devinatz, A. (1964), Toeplitz operators on H2 spaces. Trans. Amer. Math. Soc. 112, 304–317.Google Scholar
Devinatz, A. (1967), On Wiener–Hopf operators. In Functional Analysis (Irvine, CA, 1966) (ed. B. R. Gelbaum), pp. 81–118. Thompson, Washington, DC.Google Scholar
Devinatz, A. and Shinbrot, M. (1969), General Wiener–Hopf operators. Trans. Amer. Math. Soc. 145, 467–494.Google Scholar
DeVore, R. A. and Lorentz, G. G. (1993), Constructive Approximation. Springer, Berlin and Heidelberg.Google Scholar
Dieudonné, J. (1943), Sur les homomorphismes d’espaces normés. Bull. Sci. Math. (2) 67, 72–84.Google Scholar
Dieudonné, J. (1975), Jules-Henri Poincaré. In Dictionary of Scientific Biography, vol. XI (ed. C. C. Gillespie). Scribner, New York.Google Scholar
Dieudonné, J. (1981), History of Functional Analysis. vol. 49 of North-Holland Math. Studies. North-Holland, Amsterdam.Google Scholar
Dixmier, J. (1996), Les C*-algèbres et leurs représentations. Gauthier-Villars, Paris.Google Scholar
Douady, A. (1965), Un espace de Banach dont le groupe linéaire n’est pas connexe. Indag. Math. 68, 787–789.Google Scholar
Douglas, J. (1931), Solution of the problem of Plateau. Trans. Amer. Math. Soc. 33:1, 263–321.Google Scholar
Douglas, R. G. (1968a), On the spectrum of a class of Toeplitz operators. J. Math. Mech. Indiana Univ. 18, 433–436.Google Scholar
Douglas, R. G. (1968b), Toeplitz and Wiener–Hopf operators in H + C. Bull. Amer. Math. Soc. 75, 895–899.Google Scholar
Douglas, R. G. (1969a), On the operator equations S*XT = X and related topics. Acta Sci. Math. Szeged 30(1–2), 19–32.Google Scholar
Douglas, R. G. (1969b), On the spectrum of Toeplitz and Wiener–Hopf operators. In Abstract Spaces and Approximation Theory (ed. P. L. Butzer and B. Szökefalvi-Nagy), pp. 53–66. Birkhäuser, Basel and Stuttgart.Google Scholar
Douglas, R. G. (1972), Banach Algebra Techniques in Operator Theory. Academic Press, New York and London.Google Scholar
Douglas, R. G. (1973), Banach Algebra Techniques in the Theory of Toeplitz Operators, vol. 15 of CBMS Regional Conference Series in Mathematics. American Mathematical Society, Providence, RI.CrossRefGoogle Scholar
Douglas, R. G. (1980), C*-Algebra Extensions and K-Homology. Princeton University Press.Google Scholar
Douglas, R. G. and Rudin, W. (1969), Approximation by inner functions. Pacif. J. Math. 31, 313–320.Google Scholar
Douglas, R. G. and Sarason, D. (1970), Fredholm Toeplitz operators. Proc. Amer. Math. Soc. 26, 117–120.Google Scholar
Douglas, R. G. and Taylor, J. L. (1972), Wiener–Hopf operators with measure kernels. In Hilbert Space Operators and Operator Algebras (Tihany, 1970), vol. 5 of Colloquia Mathematica Societatis János Bolyai, pp. 135–141. North-Holland, Amsterdam.Google Scholar
Douglas, R. G. and Widom, H. (1970), Toeplitz operators with locally sectorial symbols. Indiana Univ. Math. J. 20, 385–388.Google Scholar
Duduchava, R. (1979), Integral Equations with Fixed Singularities. Teubner, Leipzig.Google Scholar
Dunford, N. and Schwartz, J. (1958), Linear Operators, part 1: General Theory. Wiley (Interscience), New York.Google Scholar
Duoandikoetxea, J. (2001), Fourier Analysis. American Mathematical Society, Providence, RI.Google Scholar
Durbin, J. (1960), The fitting of time series models. Revue de l’Institut International de Statistique 28, 233–44.Google Scholar
Dym, H. and McKean, H. P. (1976), Gaussian Processes, Function Theory and the Inverse Spectral Problem. Academic Press, New York.Google Scholar
Edwards, R. E. and Gaudry, G. I. (1977), Littlewood–Paley and Multiplier Theory. Springer, Berlin.Google Scholar
Ehrhardt, T. (2003), A generalization of Pincus’ formula and Toeplitz operator determinants. Arch. Math. (Basel) 80, 302–309.Google Scholar
Fatou, P. (1906), Séries trigonométriques et séries de Taylor. Acta Math. 30, 335–400.Google Scholar
Fedosov, B. V. (1970), A direct proof of the index formula for an elliptic system on Euclidean space. Funct. Anal. Appl. 4:4, 83–84.Google Scholar
Fefferman, C. (1971), Characterizations of bounded mean oscillation. Bull. Amer. Math. Soc. 77:4, 587–588.Google Scholar
Fefferman, C. and Stein, E. (1972), Hp spaces of several variables. Acta Math. 129:3–4, 137–193.Google Scholar
Ferguson, S. and Lacey, M. (2002), A characterization of product BMO by commutators. Acta Math. 189, 143–160.Google Scholar
Fischer, E. (1911), Über das Carathéodorische Problem, Potenzreihen mit positiven reellen Teil betreffend. Rendiconti Circ. Mat. Palermo 32, 240–256.Google Scholar
Fisher, M. and Hartwig, R. (1968), Toeplitz determinants: some applications, theorems, and conjectures. Adv. Chem. Phys. 15, 333–353.Google Scholar
Foias, C. and Frazho, A. E. (1990), The Commutant Lifting Approach to Interpolation Problems, vol. 44 of Operator Theory: Advances and Applications. Birkhäuser, Basel.Google Scholar
Foias, C., Frazho, A. E., Gohberg, I., and Kaashoek, M. A. (1998), Metric Constrained Interpolation, Commutant Lifting and Systems. Birkhäuser, Basel.Google Scholar
Fredholm, I. (1900), Sur une nouvelle méthode pour la résolution du probléme de Dirichlet. Kong. Vetenskaps-Akad. Fbrh. Stockholm, 39–46.Google Scholar
Fredholm, I. (1903), Sur une classe d’équations fonctionnelles. Acta Math. 27, 365–390.Google Scholar
Gakhov, F. D. (1963), Boundary Value Problems. Dover, New York (1990). Russian original: Fizmatgiz, Moscow (1963).Google Scholar
Gakhov, F. D. and Chersky, Y. I. (1978), Equations of Convolution Type. Fizmatgiz, Moscow.Google Scholar
Gantmacher, F. R. (1966), The Theory of Matrices (in Russian), second edition. Nauka, Moscow. English translation: Chelsea Publishing, New York (1960).Google Scholar
Garnett, J. B. (1981), Bounded Analytic Functions. Academic Press, New York.Google Scholar
Garcia, S. R. and Ross, W. T. (2012), Recent progress on truncated Toeplitz operators. arXiv:1108.1858v4Google Scholar
Garsia, A. (1971), A presentation of Fefferman theorem. Unpublished.Google Scholar
Gelfand, I. M. (1960), On elliptic equations (in Russian). Uspekhi Mat. Nauk 15:3, 121–132. English translation: Russ. Math. Surv. 15:3 (1960), 113–123.Google Scholar
Gelfand, I. M., Raikov, D. A., and Shilov, G. E. (1960), Commutative Normed Rings (in Russian). Fizmatgiz, Moscow. English translation: Chelsea Publishing, New York (1964).Google Scholar
Gelfand, I. M. and Vilenkin, N. Y. (1961), Generalized Functions, vol. 4: Some Applications of Harmonic Analysis (in Russian). Fizmatgiz, Moscow. English translation: Academic Press, New York (1964).Google Scholar
Georgiadou, M. (2004), Constantin Carathéodory: Mathematics and Politics in Turbulent Times. Springer, Berlin and Heidelberg.Google Scholar
Geronimo, J. S. and Case, K. M. (1979), Scattering theory for polynomials orthogonal on the unit circle. J. Math. Phys. 20, 299–310.Google Scholar
Glazman, I. M. and Lyubich, Y. I. (1969), Finite-dimensional Linear Analysis (in Russian). Nauka, Moscow. English translation: Finite-dimensional Linear Analysis: A Systematic Presentation in Problem Form, MIT Press, Cambridge, MA (1974).Google Scholar
Gohberg, I. C. (1951a), On linear equations in normed spaces. Dokl. Akad. Nauk USSR 76, 477–480.Google Scholar
Gohberg, I. C. (1951b), On linear operators analytically depending on a parameter. Dokl. Akad. Nauk USSR 78:4, 620–632.Google Scholar
Gohberg, I. (1964), Factorization problem in normed rings, functions of isometric and symmetric operators, and singular integral equations. Uspekhi Mat. Nauk 19:1, 71–124.Google Scholar
Gohberg, I. (2004), The Atiyah–Singer index formula. Nieuwe Archief voor Wiskunde 5/5, no. 4, December 2004, p. 319 (Letters to the editor).Google Scholar
Gohberg, I. C. and Feldman, I. A. (1967), Convolution Equations and Projection Methods for their Solutions. Moldavian Academy, Kishinev (1967), and Nauka, Moscow (1971). English translation: vol. 41 of Translations of Mathematical Monographs, American Mathematical Society, Providence, RI (1974).Google Scholar
Gohberg, I. C. and Feldman, I. A. (1968), On Wiener–Hopf integro-difference equations (in Russian). Doklady Akad. Nauk SSSR 183:1, 25–28. English translation: Soviet Math. Doklady 9 (1968), 1312–1316.Google Scholar
Gohberg, I., Goldberg, S., and Kaashoek, M. A. (1990), Classes of Linear Operators, vol. I. Birkhäuser, Basel.Google Scholar
Gohberg, I., Goldberg, S., and Krupnik, N. (1996), Traces and determinants of linear operators. Integral Equations Oper. Theory 26:2, 136–187.Google Scholar
Gohberg, I., Kaashoek, M. A., and Spitkovsky, I. M. (2003), An overview of matrix factorization theory and operator applications. In Factorization and Integrable Systems (ed. I. Gohberg, Manojlovic, N., and A. Ferreira dos Santos), vol. 141 of Operator Theory: Advances and Applications, pp. 1–102. Birkhäuser, Basel.Google Scholar
Gohberg, I. C. and Krein, M. G. (1957), The basic propositions on defect numbers, root numbers and indices of linear operators (in Russian). Uspekhi Mat. Nauk 12:2, 43–118. English translation: Amer. Math. Soc. Transl. (2) 13 (1960), 185–264.Google Scholar
Gohberg, I. C. and Krein, M. G. (1958), Systems of integral equations on a half-line with kernel depending upon the difference of the arguments (in Russian). Uspekhi Mat. Nauk 13:2(80), 3–72. English translation: Amer. Math. Soc. Transl. 14 (1960), 217–287.Google Scholar
Gohberg, I. and Krupnik, N. Y. (1969), On the algebra generated by Toeplitz matrices (in Russian). Funktsional. Analiz i Prilozhen 3:2, 46–56. English translation: Funct. Anal. Appl. 3:2 (1969), 119–127.Google Scholar
Gohberg, I. and Krupnik, N. (1973), One-dimensional Linear Singular Integral Equations (in Russian). Shtiintsa, Kishinev. English translation, vols, I and II: Birkhäuser, Basel (1992).Google Scholar
Gohberg, I. and Sementsul, A. (1972), On the inversion of finite Toeplitz matrices and their continuous analogues (in Russian). Matem. Issledovania (Kishinev) 7:2, 272–283.Google Scholar
Golinskii, B. and Ibragimov, I. (1971), On Szegö’s limit theorem. Math. URSS Izvestia 5:2, 421–446.Google Scholar
Golub, G. H. and C. F. Van Loan (1996), Matrix Computations, third edition. Johns Hopkins University Press, Baltimore.Google Scholar
Grafakos, L. (2008), Classical Fourier Analysis, second edition. Springer.Google Scholar
Gray, R. M. (2005), Toeplitz and circulant matrices: a review. Found. Trends Commun. Inform. Theory 2:3, 155–239.Google Scholar
Grenander, U. and Szegö, G. (1958), Toeplitz Forms and Their Applications. University of California Press, Berkeley.Google Scholar
Grothendieck, A. (1956), La théorie de Fredholm. Bull. Soc. Math. France 84, 319–384.Google Scholar
Hadamard, J. (1893), Sur le module maximum que puisse atteindre un déterminant. CR Acad. Sci. Paris 116, 1500–1501. See also pp. 239–245 of Œuvres de Jacques Hadamard, vol. I, CNRS, Paris (1968).Google Scholar
Hardy, G. H. (1908), The theory of Cauchy’s principal values. Proc. London Math. Soc. 7:2, 181–208.Google Scholar
Hardy, G. H., Littlewood, J. E., and Pólya, G. (1934), Inequalities. Cambridge University Press.Google Scholar
Harrell, E. M. II (2004), A short history of operator theory. www.mathphysics.com/opthy/OpHistory.htmlGoogle Scholar
Hartman, P. (1958), On completely continuous Hankel matrices. Proc. Amer. Math. Soc. 9, 862–866.Google Scholar
Hartman, P. and Wintner, A. (1950a), On the spectra of Toeplitz matrices. Amer. J. Math. 72, 359–366.Google Scholar
Hartman, P. and Wintner, A. (1950b), On the essential spectra of singular eigenvalue problems. Amer. J. Math. 72, 545–552.Google Scholar
Hartman, P. and Wintner, A. (1954), The spectra of Toeplitz’s matrices. Amer. J. Math. 76, 867–882.Google Scholar
Hausdorff, F. (1932), Zur Theorie der linearen metrischen Räume. J. Reine Angew. Math. 167, 294–311.Google Scholar
Havin, V. P. and Nikolski, N. K. (2000), Stanislav Aleksandrovich Vinogradov, his life and mathematics. In Complex Analysis, Operators, and Related Topics: The S. A. Vinogradov Memorial Volume (ed. V. Havin and N. Nikolski), vol. 113 of Operator Theory: Advances and Applications, pp. 1–18. Birkhäuser, Basel.Google Scholar
Hedenmalm, H., Korenblum, B., and Zhu, K. (2000), Theory of Bergman Spaces. Springer, New York and Heidelberg.Google Scholar
Heinig, G. and Rost, K. (1984), Algebraic Methods for Toeplitz-like Matrices and Operators. Birkhäuser, Basel.Google Scholar
Helson, H. (1964), Lectures on Invariant Subspaces. Academic Press, New York.Google Scholar
Helson, H. (2010), Hankel forms. Studia Math. 198, 79–84.Google Scholar
Helson, H. and Szegö, G. (1960), A problem of prediction theory. Ann. Mat. Pura Appl. 51, 107–138.Google Scholar
Helton, J. W. and Howe, R. (1973), Integral operators: commutators, traces, index, and homology. In Proc. Conf. on Operator Theory (Halifax, 1973), vol. 345 of Lecture Notes in Mathematics, pp. 141–209. Springer, Berlin and Heidelberg.Google Scholar
Herglotz, G. (1911), Über Potenzreihen mit positiven reellen Teil im Einheitskreise. Berichte Verh. Kgl.-sächs. Gesellsch. Wiss. Leipzig, Math.-Phys. Kl. 63, 501–511.Google Scholar
Hermite, C., Poincaré, H., and Rouché, E., eds (1898), Œuvres de Laguerre, vol. 1: Algèbre, Calcul intégral (reprint of the 1898 edition). Bronx, New York (1972).Google Scholar
Hilbert, D. (1894), Ein Beitrag zur Theorie des Legendre’schen Polynoms. Acta Math. 18, 155–159.Google Scholar
Hilbert, D. (1904), Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen, Erste Mitteilung. Nachr. Acad. Wiss. Göttingen Math. Phys. Kl. II, 49–91.Google Scholar
Hilbert, D. (1912), Gründzüge einer allgemeinen Theorie der linearen Integralgleichungen. Teubner, Leipzig.Google Scholar
Hilbert, D. (1998), Œuvres choisies, vol. 2: Analyse, Physique, Problèmes, Personalia (in Russian translation) (ed. A. Parshin), Moscow.Google Scholar
Hildebrandt, T. (1928), Über vollstetige lineare Transformationen. Acta Math. 51, 311–318.Google Scholar
Hirschman, I. I. and Widder, D. V. (1955), The Convolution Transform. Princeton University Press (Dover edition, 2005).Google Scholar
Hoffman, K. (1962), Banach Spaces of Analytic Functions. Prentice Hall, Englewood Cliffs, NJ.Google Scholar
Hoffman, K. and Singer, I. M. (1960), Maximal algebras of continuous functions. Acta Math. 103, 217–241.Google Scholar
Hörmander, L. (1960), Estimates for translation invariant operators in Lp spaces. Acta Math. 104, 93–140. L. Hörmander (1971), On the index of pseudo-differential operators. In Elliptische Differentialgleichungen, vol. II, pp. 127–146. Akademie, Berlin.Google Scholar
Hörmander, L. (1985), The Analysis of Linear Partial Differential Operators, vol. III: Pseudo-differential Operators. Springer, Berlin.Google Scholar
Hurwitz, A. (1901), Sur le problème des isopérimètres. CR Acad. Paris 132, 401–403.Google Scholar
Hytönen, T. P. (2009), A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa. arXiv:0909.3231v1Google Scholar
Iokhvidov, I. S. (1974), Hankel and Toeplitz Matrices and Forms: Algebraic Theory. Nauka, Moscow.Google Scholar
Ismagilov, R. S. (1963), On the spectrum of Toeplitz matrices. Dokl. Akad. Nauk SSSR 149:4, 769–772.Google Scholar
Its, A. R. (2003), The Riemann–Hilbert problem and integrable systems. Notices Amer. Math. Soc. 50:11, 1389–1400.Google Scholar
Johansson, K. (1988), On Szegö’s asymptotic formula for Toeplitz determinants and generalizations. Bull. Soc. Math. (2) 112, 257–304.Google Scholar
John, F. (1961), Rotation and strain. Comm. Pure Appl. Math. 14:3, 391–413.Google Scholar
John, F. and Nirenberg, L. (1961), On functions of bounded mean oscillation. Comm. Pure Appl. Math. 14:3, 415–426.Google Scholar
Julia, G. (1944), Sur la représentation analytique des opérateurs bornés ou fermés de l’espace hilbertien. CR Acad. Sci. Paris 219, 225–227.Google Scholar
Kac, M. (1954), Toeplitz matrices, translation kernels and a related problem in probability theory. Duke Math. J. 21, 501–509.Google Scholar
Kailath, T. and Sayed, A. H., eds (1999), Fast Reliable Algorithms for Matrices with Structure. SIAM, Philadelphia.Google Scholar
Katznelson, Y. (1976), An Introduction to Harmonic Analysis. Dover, New York.Google Scholar
Kesten, H. (1961), Random walk with absorbing barriers and Toeplitz forms. Illinois J. Math. 5, 267–290.Google Scholar
Khrushchev, S. V. (1977), Entropy meaning of summability of the logarithm (in Russian). Zapiski Nauchn. Seminarov LOMI (Steklov Math. Inst.) 73, 152–187. English translation: J. Soviet Math. 34:6 (1986), 212-233.Google Scholar
Klemes, I. (2001), Finite Toeplitz matrices and sharp Littlewood conjectures. In memoriam: Thomas H. Wolff. Algebra i Analiz (St. Petersburg Math. J.) 13:1, 39–59.Google Scholar
Kolmogorov, A. N. (1941), Stationary sequences in Hilbert space (in Russian). Bull. Moscow Univ. Math. 2:6, 1–40.Google Scholar
Koosis, P. (1980), Introduction to Hp Spaces. Cambridge University Press.Google Scholar
Kozak, A. V. (1973), A local principle in the theory of projection methods (in Russian). Dokl. Acad. Sci. URSS 212:6, 1287–1289. English translation: Soviet Math. Dokl. 14 (1974), 1580–1583.Google Scholar
Kra, I. and Simanca, S. (2012), On circulant matrices. Notices Amer. Math. Soc. 59:3, 368–377.Google Scholar
Krein, M. (1947a), The theory of self-adjoint extensions of semi-bounded Hermitian operators and applications, I. Mat. Sbornik 20, 431–495.Google Scholar
Krein, M. (1947b), The theory of self-adjoint extensions of semi-bounded Hermitian operators and applications, II. Mat. Sbornik 21, 365–404.Google Scholar
Krein, M. (1958), Integral equations on a half-line with kernel depending upon the difference of the arguments (in Russian). Uspekhi Mat. Nauk 13:5, 3–120. English translation: Amer. Math. Soc. Transl. (2) 22 (1962), 163–288.Google Scholar
Krein, M. (1966), On some new Banach algebras and Wiener–Lévy type theorems for Fourier series and integrals (in Russian). Matem. Issledovania (Kishinev) 1 (1966), 82–109. English translation: Amer. Math. Soc. Transl. 93 (1970), 177–199.Google Scholar
Krein, M. and Krasnoselskii, M. (1952), Stability of the index of an unbounded operator (in Russian). Mat. Sbornik 30:1, 219–224.Google Scholar
Kronecker, L. (1881), Zur Theorie der Elimination einer Variablen aus zwei algebraischen Gleichungen. Monatsber. Königl. Preussischen Akad. Wiss. (Berlin) (1881), 535–600.Google Scholar
Krupnik, N. Y. (1984), Banach Algebras with Symbol and Singular Integral Operators (in Russian). Shtiintsa, Kishinev. English translation: Birkhäuser, Basel (1987).Google Scholar
Krupnik, N. Y. and Feldman, I. A., (1985), Relations between factorization and invertibility of finite Toeplitz matrices (in Russian). Izvestia AN Moldavskoi SSR Ser. Phys.-Tech. i Math. 3, 20–26.Google Scholar
Kuipers, L. and Niederreiter, H. (1974), Uniform Distribution of Sequences. Wiley (Dover edition, 2006).Google Scholar
Lacey, M. (2013a), The two weight inequality for the Hilbert transform: a primer. arXiv:1304.5004Google Scholar
Lacey, M. (2013b), Two weight inequality for the Hilbert transform: a real variable characterization, II. arXiv:1301.4663Google Scholar
Lacey, M. and Terwilleger, E. (2009), Hankel operators in several complex variables and product, BMO. Houston J. Math. 35, 159–183.Google Scholar
Landau, E. (1913), Abschätzung der Koeffizientensumme einer Potenzreihe. Arch. Math. Phys. 21, 42–50, 250–255.Google Scholar
Landkof, N. S. (1972), Foundations of Modern Potential Theory. Springer.Google Scholar
Landsberg, G. (1910), Theorie der Elementarteiler linearer Integralgleichungen. Math. Ann. 69, 227–265.Google Scholar
Lawrie, J. B. and Abrahams, I. D. (2007), A brief historical perspective of the Wiener–Hopf technique. J. Engrg. Math. 59:4, 351–358.Google Scholar
Lebesgue, H. (1906), Leçons sur les séries trigonométriques. Gauthier-Villars, Paris.Google Scholar
Lee, Y. W. (1960), Statistical Theory of Communications. Wiley, New York.Google Scholar
Levinson, N. (1947), The Wiener RMS error criterion in filter design and prediction. J. Math. Phys. 25, 261–78.Google Scholar
Libkind, L. M. (1972), On asymptotics of the eigenvalues of Toeplitz forms (in Russian). Mat. Zametki 11:2, 151–158.Google Scholar
Lindelöf, E. (1905), Le calcul des résidues et ses applications à la théorie des fonctions. Gauthier-Villars, Paris (Chelsea Publishing edition, 1947).Google Scholar
Lindenstrauss, J. and Tzafriri, L. (1977), Classical Banach Spaces, vol. I. Springer, Berlin.Google Scholar
Lindenstrauss, J. and Tzafriri, L. (1979), Classical Banach Spaces, vol. II. Springer, Berlin.Google Scholar
Linton, C. M. and McIver, P. (2001), Handbook of Mathematical Techniques for Wave/Structure Interactions. CRC Press.Google Scholar
Litvinchuk, G. S. and Spitkovsky, I. (1987), Factorization of Measurable Matrix Functions. Akademie, Berlin, and Birkhäuser, Basel.Google Scholar
Loomis, L. H. (1953), An Introduction to Abstract Harmonic Analysis. Van Nostrand, Toronto.Google Scholar
Lorch, L. (1954), The principal term in the asymptotic expansion of the Lebesgue constants. Amer. Math. Monthly 61, 245–249.Google Scholar
Luzin, N. N. (1913), Sur la convergence des séries trigonométriques de Fourier. CR Acad. Sci. Paris 156, 1655–1658.Google Scholar
Luzin, N. N. (1915), L’intégrale et les séries trigonométriques (in Russian). University of Moscow (reproduced in Mat. Sbornik 30:1 (1916), 1–242). Second edition: Izd. Akad. Nauk SSSR (1951).Google Scholar
Marshall, D. E. (1976), Subalgebras of L containing H. Acta Math. 137, 91–98.Google Scholar
Maz’ya, V. and Verbitsky, I. (2002), The Schrödinger operator on the energy space: boundedness and compactness criteria. Acta Math. 188, 263–302.Google Scholar
Mei, T. (2007), Operator Valued Hardy Spaces, vol. 881 of Memoirs of the American Mathematical Society. American Mathematical Society, Providence, RI.Google Scholar
Mikhlin, S. G. (1936), Composition of singular integrals. Doklady Akad. Nauk SSSR 2(II):1(87), 3–6.Google Scholar
Mikhlin, S. G. (1948), Singular integral equations. Uspekhi Mat. Nauk 3:3, 29–112.Google Scholar
Mikhlin, S. G. (1962), Multivariate Singular Integrals and Integral Equations (in Russian). GIFML, Moscow. English translation: Pergamon Press, Oxford (1965).Google Scholar
Mingarelli, A. B. (2005), A glimpse into the life and times of F. V. Atkinson. Math. Nachrichten 278:12–13, 1364–1387.Google Scholar
Mityagin, B. S. (1970), Homotopy structure of the linear group of a Banach space. Uspekhi Mat. Nauk 25:5, 63–106.Google Scholar
Murphy, G. J. (1990), C*-algebras and Operator Theory. Academic Press, Boston.Google Scholar
Muskhelishvili, N. I. (1947), Singular Integral Equations: Boundary Problems of Function Theory and their Application to Mathematical Physics (in Russian), first edition Moscow. English translation: Dover, second edition (1992).Google Scholar
Nazarov, F. (1997), A counterexample to Sarason’s conjecture. www.math.msu.edu/126fedja/prepr.htmlGoogle Scholar
Nazarov, F., Pisier, G., Treil, S., and Volberg, A. (2002), Sharp estimates in vector Carleson imbedding theorem and for vector paraproducts. J. Reine Angew. Math. 542, 147–171.Google Scholar
Nazarov, F., Treil, S., and Volberg, A. (2004), Two weight estimate for the Hilbert transform and Corona decomposition for non-doubling measures. arXiv:1003.1596Google Scholar
Nehari, Z. (1957), On bounded bilinear forms. Ann. of Math. 65, 153–162.Google Scholar
Neumann, C. (1877), Untersuchungen über das logarithmische und Newton’sche Potential. Teubner, Leipzig.Google Scholar
Nikol’skaya, L. N. and Farforovskaya, Y. B. (2003), Toeplitz and Hankel matrices as Hadamard–Schur multipliers. Algebra i Analiz (St. Petersburg Math. J.) 15:6, 141–160.Google Scholar
Nikolski, N. (1985), Ha-plitz operators: a survey of some recent results. In Operators and Function Theory, vol. 153 of NATO ASI Series, Math. Phys. (ed. S. Power), pp. 87–138. Reidel, Dordrecht.Google Scholar
Nikolski, N. (1986), Treatise on the Shift Operator. Springer, Berlin.Google Scholar
Nikolski, N. (2002a), Operators, Functions, and Systems, vol. 1. American Mathematical Society, Providence, RI.Google Scholar
Nikolski, N. (2002b), Operators, Functions, and Systems, vol. 2. American Mathematical Society, Providence, RI.Google Scholar
Nikolski, N. (2002c), On the Norm of a Finite Toeplitz Matrix. Lecture notes, Michigan State University (unpublished).Google Scholar
Nikolski, N. (2012), Espaces de Hardy. Belin.Google Scholar
Nikolski, N. (2019), Hardy Spaces. Cambridge University Press.Google Scholar
Nikol’sky, S. M. (1943), Linear equations in linear normed spaces (in Russian). Izvetia Akad. Nauk SSSR Ser. Mat. 7:3, 147–166.Google Scholar
Noble, B. (1998), Methods Based on the Wiener–Hopf Technique for the Solution of Partial Differential Equations. Chelsea Publishing (editions 1958, 1988, 1998).Google Scholar
Noether, F. (1921), Über eine Klasse singulärer Integralgleichungen. Math. Ann. 82, 42–63.Google Scholar
Ortega-Cerdà, J. and Seip, K. (2012), A lower bound in Nehari’s theorem on the polydisc. J. Anal. Math. 118:1, 339–342.Google Scholar
Page, L. B. (1970), Bounded and compact vectorial Hankel operators. Trans. Amer. Math. Soc. 150, 529–539.Google Scholar
Parrott, S. (1978), On a quotient norm and the Sz.-Nagy–Foias lifting theorem. J. Funct. Anal. 30, 311–328.Google Scholar
Peetre, J. (1989), The Berezin Transform and Ha-plitz Operators. Math. Institute Reports, Lund University.Google Scholar
Peller, V. V. (1980), Hankel operators of class Sp and their applications (rational approximation, Gaussian processes, the problem of majorization of operators) (in Russian). Mat. Sbornik 113(155):4, 538–581. English translation: Math. USSR Sbornik 41 (1982), 443–479.Google Scholar
Peller, V. V. (2003), Hankel Operators and their Applications. Springer, New York.Google Scholar
Petermichl, S. (2000), Dyadic shifts and a logarithmic estimate for Hankel operators with matrix symbol. CR Acad. Sci. Paris Ser. I Math. 330, 455–460.Google Scholar
Petersen, K. E. (1977), Brownian Motion, Hardy Spaces and Bounded Mean Oscillation. Cambridge University Press.Google Scholar
É. Picard (1927), Leçons sur quelques types simples d’équations aux dérivées partielles. Paris.Google Scholar
Pietsch, A. (2007), History of Banach Spaces and Linear Operators. Birkhäuser, Boston.Google Scholar
Plemelj, J. (1908a), Ein Ergänzungssatz zur Cauchyschen Integraldarstellung analytischer Funktionen, Randwerte betreffend. Monatsheft für Math. Phys. XIX, 205–210.Google Scholar
Plemelj, J. (1908b), Riemannsche Funktionenscharen mit gegebener Monodromiegruppe. Monatsheft für Math. Phys. XIX, 211–245.Google Scholar
Poincaré, H. (1895), La méthode de Neumann et le problème de Dirichlet. Acta Math. 20 (1896–1897), 59–142. Reprinted in Œuvres de Henri Poincaré, vol. 9, pp. 202–272, Gauthier-Villars, Paris.Google Scholar
Poincaré, H. (1908), Science et méthode. Flammarion, Paris.Google Scholar
Poincaré, H. (1910a), Leçons de Mécanique Céleste, vol. 3. Gauthier-Villars, Paris.Google Scholar
Poincaré, H. (1910b), Remarques diverses sur l’équation de Fredholm. Acta Math. 33, 57–86.Google Scholar
Pólya, G. (1914), Question 4340. L’Intermédiaire des mathématiciens 21, 27.Google Scholar
Pólya, G. and Szegö, G. (1925), Aufgaben und Lehrsatze aus der Analysis, vols 1, 2. Springer, Berlin. Russian translation: GITTL, Moscow (1948). English translation: Springer, Berlin and New York (1972).Google Scholar
Power, S. C. (1980), Hankel operators on Hilbert space. Bull. London Math. Soc. 12, 422–442.Google Scholar
Power, S. C. (1982), Hankel Operators on Hilbert Space, vol. 64 of Pitman Research Notes in Mathematics. Pitman, Boston.Google Scholar
Power, S. C. (1984), Quasinilpotent Hankel operators. In Linear and Complex Analysis Problem Book (ed. V. Havin and N. Nikolski), vol. 1043 of Lecture Notes in Mathematics, pp. 259–261. Springer.Google Scholar
Privalov, I. I. (1919), L’intégrale de Cauchy (in Russian). Thesis, University of Saratov.Google Scholar
Privalov, I. I. (1941), Boundary Properties of Analytic Functions (in Russian). Second edition: GITTL, Moscow (1950). German translation: Deutscher Verlag, Berlin (1956).Google Scholar
Prössdorf, S. and Silbermann, B. (1991), Numerical Analysis for Integral and Related Operator Equations. Birkhäuser, Basel.Google Scholar
Radon, J. (1919), Über lineare Funktionaltransformationen und Funktionalgleichungen. Sitzungsber. Akad. Wiss. Wien, math.-naturw. Kl., Abt. Ha 128, 1083–1121.Google Scholar
Rambour, P. and Rinkel, J.-M. (2007), Un théorème de Spitzer–Stone fort pour une matrice de Toeplitz à symbole singulier défini par une classe de fonctions analytiques. Ann. Fac. Sci. Toulouse Math. 6:16, 331–367.Google Scholar
Rambour, P. and Seghier, A. (2012), Inversion des matrices de Toeplitz dont le symbole admet un zéro d’ordre rationnel positif, valeur propre minimale. Ann. Fac. Sci. Toulouse Math. (6) 21:1, 173–211.Google Scholar
Rappoport, I. M. (1948a), On a class of singular integral equations (in Russian). Doklady Akad. Nauk SSSR 59:8, 1403–1406.Google Scholar
Rappoport, I. M. (1948b), On a class of infinite systems of algebraic linear equations (in Ukrainian). Doklady Ukrainian Akad. Nauk Fiz.-Mat. and Chimical Sci. 3, 6–10.Google Scholar
Reed, M. and Simon, B. (1972), Methods of Modern Mathematical Physics, vol. I: Functional Analysis. Academic Press, New York.Google Scholar
Reed, M. and Simon, B. (1978), Methods of Modern Mathematical Physics, vol. IV: Analysis of Operators. Academic Press, New York.Google Scholar
Reid, C. (1970), Hilbert, With an Appreciation of Hilbert’s Mathematical Work by Hermann Weyl. Springer, Berlin and Heidelberg.Google Scholar
Riemann, B. (1876), Gesammelte mathematische Werke und wissenschaftlicher Nachlass (ed. R. Dedekind and H. Weber), Teubner, Leipzig. http://archive.org/ details/bernardrgesamm00riemrichGoogle Scholar
Riesz, F. (1916), Über lineare Funktionalgleichungen. Acta Math. 41, 71–98.Google Scholar
Riesz, F. and Riesz, M. (1916), Über die Randwerte einer analytische Funktion. In Quatrième Congrès des Math. Scand., Stockholm, pp. 27–44.Google Scholar
Riesz, F. and Szökefalvi-Nagy, B. (1955), Leçons d’analyse fonctionnelle. Akadémiai Kiado, Szeged.Google Scholar
Riesz, M. (1949), L’intégrale de Riemann–Liouville et le problème de Cauchy. Acta Math. 81, 1–223.Google Scholar
Rochberg, R. (1987), Toeplitz and Hankel operators on the Paley–Wiener space. Integral Equations Oper. Theory 10:2, 187–235.Google Scholar
Rochberg, R. and Wu, Z. (1993), A new characterization of Dirichlet type spaces and applications. Illinois J. Math. 37:1, 101–122.Google Scholar
Rodman, L., Spitkovsky, I., and Woerdeman, H. (2002), Abstract Band Method via Factorization, Positive and Band Extensions of Multivariable Almost Periodic Matrix Functions, and Spectral Estimation, vol. 762 of Memoirs of the American Mathematical Society. American Mathematical Society, Providence, RI.Google Scholar
Rosenblum, M. (1960), The absolute continuity of Toeplitz’s matrices. Pacif. J. Math. 10, 987–996.Google Scholar
Rosenblum, M. (1965), A concrete spectral theory of self-adjoint Toeplitz operators. Amer. J. Math. 87, 709–718.Google Scholar
Rosenblum, M. and Rovnyak, J. (1985), Hardy Classes and Operator Theory. Oxford University Press.Google Scholar
Rozanov, Y. A. (1963), Stationary Stochastic Processes (in Russian). Fizmatgiz, Moscow. English translation: Holden-Day, San Francisco (1967).Google Scholar
Rudin, W. (1959), Weak almost periodic functions and Fourier–Stieltjes transforms. Duke Math. J. 26, 215–220.Google Scholar
Rudin, W. (1962), Fourier Analysis on Groups. Wiley, New York.Google Scholar
Rudin, W. (1986), Real and Complex Analysis. McGraw-Hill, New York.Google Scholar
Rudin, W. (1991), Functional Analysis. McGraw-Hill, New York. C. Runge (1885), Zur Theorie der eindeutigen analytischen Funktionen. Acta Math. 6, 229–244.Google Scholar
Ruston, A. F. (1986), Fredholm Theory in Banach Spaces. Cambridge University Press.Google Scholar
Saff, E. B. and Totik, V. (1997), Logarithmic Potentials with External Fields. Springer, Berlin and Heidelberg.Google Scholar
Sarason, D. (1967), Generalized interpolation in H. Trans. Amer. Math. Soc. 127:2, 179–203.Google Scholar
Sarason, D. (1973a), Algebras of functions on the unit circle. Bull. Amer. Math. Soc. 79, 286–299.Google Scholar
Sarason, D. (1973b), On products of Toeplitz operators. Acta Sci. Math. Szeged 35, 7–12.Google Scholar
Sarason, D. (1975), Functions of vanishing mean oscillation. Trans. Amer. Math. Soc. 207, 391–405.Google Scholar
Sarason, D. (1977a), Toeplitz operators with piecewise quasicontinuous symbols. Indiana Univ. Math. J. 26, 817–838.Google Scholar
Sarason, D. (1977b), Toeplitz operators with semi-almost periodic symbols. Duke Math. J. 44, 357–364.Google Scholar
Sarason, D. (1978), Function Theory on the Unit Circle. Virginia Polytechnic Institute and State University.Google Scholar
Sarason, D. (1994), Products of Toeplitz operators. In Linear and Complex Analysis Problem Book 3, part 1 (ed. V. Havin and N. Nikolski), vol. 1573 of Lecture Notes in Mathematics, pp. 318–319. Springer, Berlin and Heidelberg.Google Scholar
Sarason, D. (2007), Algebraic properties of truncated Toeplitz operators. Operators and Matrices (Springer) 1:4, 491–526.Google Scholar
Schauder, J. (1930), Über lineare, vollstetige Funktionaloperationen. Studia Math. 2:1, 183–196. I. Schur (1917), Über die Potenzreihen, die in Innern des Einheitskreises beschränkt sind, I. J. Reine Angew. Math. 147, 205–232.Google Scholar
Schur, I. (1918), Über die Potenzreihen, die in Innern des Einheitskreises beschränkt sind, II. J. Reine Angew. Math. 148, 122–145.Google Scholar
Shubin, M. A. (1987), Pseudo-differential Operators and Spectral Theory. Springer. First Russian edition: Nauka, Moscow (1978).Google Scholar
Siegmund-Schultze, R. (2009), Mathematicians Fleeing from Nazi Germany: Individual Fates and Global Impact. Princeton University Press.Google Scholar
Simon, B. (2005a), Trace Ideals and their Applications, vol. 120 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI.Google Scholar
Simon, B. (2005b), Orthogonal Polynomials on the Unit Circle, vol. 1: Classical Theory, vol. 54 of Colloquium Publications. American Mathematical Society, Providence, RI.Google Scholar
Simonenko, I. B. (1960), Riemann boundary problem with measurable coefficients (in Russian). Doklady Akad. Nauk SSSR 135:3, 538–541.Google Scholar
Simonenko, I. B. (1961), Riemann boundary problem for n pairs of functions with continuous coefficients. Izvestia Vyssh. Uchebn. Zaved. Mat. 1, 140–145.Google Scholar
Simonenko, I. B. (1964), A new general method for studying linear operator equations of the type of singular integral equations (in Russian). Doklady Akad. Nauk SSSR 158, 790–793.Google Scholar
Simonenko, I. B. (1965a), A new general method for studying linear operator equations of the type of singular integral equations, I (in Russian). Izvestia Akad. Nauk SSSR Ser. Mat. 29:3, 567–586.Google Scholar
Simonenko, I. B. (1965b), A new general method for studying linear operator equations of the type of singular integral equations, II (in Russian). Izvestia Akad. Nauk SSSR Ser. Mat. 29:4, 757–782.Google Scholar
Simonenko, I. B. (1968), Some general questions of the Riemann boundary problem (in Russian). Izvestia Akad. Nauk SSSR Ser. Mat. 32:5, 1138–1146. English translation: Math USSR Izvestia 2, 1091–1099.Google Scholar
Sokhotsky, Y. V. (1873), Ob opredelennykh integralakh i funktsiakh upotreblyaemykh pri razlozheniakh v ryady (On definite integrals and functions used for serial expansions). Habilitation thesis, University of St. Petersburg.Google Scholar
Spitkovsky, I. M. (1976), The problem of the factorization of measurable matrix-valued functions (in Russian). Dokl. Akad. Nauk SSSR 227:3, 576–579. English translation: Soviet. Math. Dokl. 17:2 (1976), 481–485.Google Scholar
Spitkovsky, I. M. (1980), Multipliers that do not influence factorizability (in Russian). Mat. Zametki 27:2, 291–299. English translation: Math. Notes 27 (1980), 145–149.Google Scholar
Spitzer, F. L. and Stone, C. J. (1960), A class of Toeplitz forms and their applications to probability theory. Illinois J. Math. 4, 253–277.Google Scholar
Spivak, M. (1971), Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus. Westview Press.Google Scholar
Stahl, H. and Totik, V. (1992), General Orthogonal Polynomials. Cambridge University Press.Google Scholar
Stein, E. (1993), Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals. Princeton University Press.Google Scholar
Stein, E. and Weiss, G. (1971), Introduction to Fourier analysis on Euclidean spaces. Princeton University Press.Google Scholar
Stone, M. H. (1932), Linear Transformations in Hilbert Space and their Applications to Analysis, vol. 15 of Colloquium Publications. American Mathematical Society, Providence, RI.Google Scholar
Szegö, G. (1915), Ein Grentzwertsatz über die Toeplitzschen Determinanten einer reellen positiven Funktion. Math. Ann. 76, 490–503.Google Scholar
Szegö, G. (1920), Beiträge zur Theorie der Toeplitzsche Formen, I. Math. Zeit. 6, 167–202.Google Scholar
Szegö, G. (1921a), Beiträge zur Theorie der Toeplitzsche Formen, II. Math. Zeit. 9, 167–190.Google Scholar
Szegö, G. (1921b), Über die Randwerte einer analytischen Funktion. Math. Ann. 84:3/4, 232–244.Google Scholar
Szegö, G. (1952), On certain Hermitian forms associated with the Fourier series of a positive function. In Festskrift Marcel Riesz (Lund, 1952), Comm. Sém. Math. Univ. Lund, suppl. vol., pp. 222–238.Google Scholar
Szegö, G. (1954), On a theorem of C. Carathéodory. In Studies in Mathematics and Mechanics: Studies Presented to Richard von Mises, pp. 62–66. Academic Press, New York.Google Scholar
Szegö, G. (1959), Orthogonal Polynomials, second edition, vol. XXIII of Colloquium Publications. American Mathematical Society, New York.Google Scholar
Szökefalvi-Nagy, B. and Foias, C. (1967), Analyse harmonique des opérateurs de l’espace de Hilbert. Akadémiai Kiado, Budapest.Google Scholar
Taylor, J. L. (1973), Measure Algebras. American Mathematical Society, Providence, RI.Google Scholar
Toeplitz, O. (1911a), Zur Theorie der quadratischen und bilinearen Formen von unendlichvielen Veränderlichen, I: Theorie des L-Formen. Math. Ann. 70, 351–376.Google Scholar
Toeplitz, O. (1911b), Über die Fouriersche Entwickelung positiver Funktionen. Rend. Circ. Mat. Palermo 32, 191–192.Google Scholar
Tolokonnikov, V. A. (1981), Estimates in Carleson’s corona theorem, ideals of the algebra H, the problem of Szökefalvi-Nagy (in Russian). Zapiski Nauchn. Semin. LOMI 113, 178–198. English translation: J. Soviet Math. 22:6 (1983), 1814–1828.Google Scholar
Trefethen, L. N. and Embree, M. (2005), Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators. Princeton University Press.Google Scholar
Treil, S. (1987), Invertibility of Toeplitz operators does not imply applicability of the finite section method (in Russian). Dokl. Akad. Nauk SSSR 292, 563–567.Google Scholar
Treil, S. (2002), Estimates in the corona theorem and ideals of H: a problem of T. Wolff; dedicated to the memory of Thomas Wolff. J. Anal. Math. 87, 481–495.Google Scholar
Treil, S. (2012), A remark on the reproducing kernel thesis for Hankel operators. arXiv:1201.0063v2Google Scholar
Treil, S. and Volberg, A. (1994), A fixed point approach to Nehari’s problem and its applications. In vol. 71 of Operator Theory: Advances and Applications, pp. 165–186. Birkhäuser, Basel.Google Scholar
Trench, W. F. (1964), An algorithm for the inversion of finite Toeplitz matrices. J. Soc. Indust. Appl. Math. (12) 3, 515–522.Google Scholar
Verblunsky, S. (1936), On positive harmonic functions (second paper). Proc. London Math. Soc. (2) 40, 290–320.Google Scholar
Verhulst, F. (2012), Henri Poincaré: Impatient Genius. Springer.Google Scholar
Volberg, A. (1982), Two remarks concerning the theorem of S. Axler, S.-Y. A. Chang and Sarason, D.. J. Operator Theory 7, 209–218.Google Scholar
Volberg, A. (2003), Calderón–Zygmund Capacities and Operators on Nonhomogeneous Spaces, vol. 100 of CBMS Regional Conference Series in Mathematics. American Mathematical Society, Providence, RI.Google Scholar
Volterra, V. (1882), Sopra alcune condizioni caratteristiche delle funzioni di una variabile complessa. Annali di Mat. Pura Applicata (2) 11, 1–55.Google Scholar
Volterra, V. (1896), Sulla inversione degli inegrali definiti. Rend. Accad. Lincei 5, 177–185, 289–300.Google Scholar
Volterra, V. (1931), Leçons sur la théorie mathématique de la lutte pour la vie. Gauthier-Villars, Paris, 1931 (second edition, 1990).Google Scholar
Weil, A. (1940), L’intégration dans les groupes topologiques et ses applications, vol. 869 of Actualités Scientifiques et Industrielles. Hermann, Paris.Google Scholar
Wermer, J. (1953), On algebras of continuous functions. Proc. Amer. Math. Soc. 4, 866–869.Google Scholar
Weyl, H. (1910a), Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen. Math. Ann. 68, 220–269.Google Scholar
Weyl, H. (1910b), Über die Gibbs’sche Erscheinung und verwandte Konvergenzphänomene. Rendiconti Circ. Mat. Palermo 30, 377–407.Google Scholar
Weyl, H. (1944), David Hilbert and his mathematical work. Bull. Amer. Math. Soc. 50, 612–654.Google Scholar
Weyl, H. (1984), Selected Works: Mathematics and Theoretical Physics, (ed. V. Arnold and A. Parshin). Nauka, Moscow.Google Scholar
Widom, H. (1960a), Inversion of Toeplitz matrices, II. Illinois J. Math. 4, 88–99.Google Scholar
Widom, H. (1960b), Inversion of Toeplitz matrices, III. Notices Amer. Math. Soc. 7, 63.Google Scholar
Widom, H. (1960c), Singular integral equations in Lp. Trans. Amer. Math. Soc. 97, 131–160.Google Scholar
Widom, H. (1964), On the spectrum of Toeplitz operators. Pacif. J. Math. 14, 365–375.Google Scholar
Widom, H. (1973), Toeplitz determinants with singular generating functions. Amer. J. Math. 95, 333–383.Google Scholar
Widom, H. (1976), Asymptotic behavior of block Toeplitz matrices and determinants, II. Adv. Math. 21, 1–29.Google Scholar
Wiener, N. (1933), The Fourier Integral and Certain of its Applications. Cambridge University Press, New York.Google Scholar
Wiener, N. (1966), Norbert Wiener, 1894–1964. Special issue of Bull. Amer. Math. Soc. (ed. F. Browder, Spanier, E., and M. Gerstenhaber) 72:1, part, II.Google Scholar
Wiener, N. and Hopf, E. (1931), Über eine Klasse singulären Integralgleichungen. S.-B. Preuss Akad. Wiss. Berlin, Phys.-Math. Kl. 30/32, 696–706.Google Scholar
Wirtinger, W. (1897), Beiträge zur Riemann’s Integrationsmethode für hyperbolische Differentialgleichungen, und deren Anwendungen auf Schwingungsprobleme. Math. Ann. 48, 364–389.Google Scholar
Wolff, T. H. (1983), Counterexamples to two variants of the Helson–Szegö theorem. Report 11, CalTech, Pasadena. Published in J. Anal. Math. 88:1 (2002), 41–62.Google Scholar
Wu, Z. (1998), Function theory and operator theory on the Dirichlet space. In Holomorphic Spaces (ed. S. Axler, McCarthy, J. E., and D. Sarason), vol. 33 of MSRI Publications, pp. 179–199. Cambridge University Press.Google Scholar
Xia, D. (1983), Spectral Theory of Hyponormal Operators. Birkhäuser, Basel.Google Scholar
Yood, B. (1951), Properties of linear transformations preserved under addition of a completely continuous transformation. Duke Math. J. 18, 599–612.Google Scholar
Yosida, K. (1940), Quasi-completely-continuous linear functional operations. In Collected Papers, Faculty of Science, Osaka Imperial University, Ser. A. Math. 7 (1939 (1940)), 297–301.Google Scholar
Zhu, K. (2007), Operator Theory in Function Spaces, second edition. American Mathematical Society, Providence, RI.Google Scholar
Zygmund, A. (1959), Trigonometric Series, vols, I and II. Cambridge University Press.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×