Skip to main content Accessibility help
×
Home
Hostname: page-component-684899dbb8-8hm5d Total loading time: 0.703 Render date: 2022-05-18T09:20:12.857Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true }

Bibliography

Published online by Cambridge University Press:  01 June 2018

Tullio Ceccherini-Silberstein
Affiliation:
Università degli Studi del Sannio, Italy
Fabio Scarabotti
Affiliation:
Università degli Studi di Roma 'La Sapienza', Italy
Filippo Tolli
Affiliation:
Università Roma Tre, Italy
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Discrete Harmonic Analysis
Representations, Number Theory, Expanders, and the Fourier Transform
, pp. 555 - 562
Publisher: Cambridge University Press
Print publication year: 2018

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

[1] A., Abdollahi and A., Loghman, On one-factorizations of replacement products, Filomat 27 (2013), no. 1, 57–63.Google Scholar
[2] R.C., Agarwal and J.W., Cooley, New algorithms for digital convolution, IEEE Trans. Acoust. Speech, Signal Processing, ASS-25, 392–410.
[3] L.V., Ahlfors, Complex analysis. An introduction to the theory of analytic functions of one complex variable. Third edition. International Series in Pure and Applied Mathematics. McGraw-Hill Book Co., New York, 1978.Google Scholar
[4] S., Ahmad, Cycle structure of automorphisms of finite cyclic groups, J. Combinatorial Theory 6 (1969), 370–374.Google Scholar
[5] M., Aigner and G.M., Ziegler, Proofs from The Book. Fifth edition. Springer-Verlag, Berlin, 2014.Google Scholar
[6] M., Ajtai, J., Komlos, and E., Szemeredi, An O(n log n) sorting network. Proceedings of the 15th Annual ACM Symposium on Theory of Computing, pp. 1–9, (1983).
[7] N., Alon, Eigenvalues and expanders, Combinatorica 6 (1986), 83–96.Google Scholar
[8] N., Alon, A., Lubotzky, and A., Wigderson, Semi-direct product in groups and zig-zag product in graphs: connections and applications (extended abstract). 42nd IEEE Symposium on Foundations of Computer Science (Las Vegas, NV, 2001), 630–637, IEEE Computer Soc., Los Alamitos, CA, 2001.Google Scholar
[9] N., Alon and V.D., Milman, ƛ1, isoperimetric inequalities for graphs, and superconcentrators, J. Combin. Theory Ser. B 38 (1985), no. 1, 73–88.Google Scholar
[10] N., Alon, O., Schwartz, and A., Shapira, An elementary construction of constant-degree expanders, Combin. Probab. Comput. 17 (2008), no. 3, 319–327.Google Scholar
[11] N., Alon and J.H., Spencer, The probabilistic method. Third edition. With an appendix on the life and work of Paul Erdos. Wiley-Interscience Series in Discrete Mathematics and Optimization. John Wiley & Sons, Inc., Hoboken, NJ, 2008.Google Scholar
[12] J.L., Alperin and R.B., Bell, Groups and representations. Graduate Texts in Mathematics, 162. Springer-Verlag, New York, 1995.Google Scholar
[13] T.M., Apostol, Introduction to analytic number theory. Undergraduate Texts inMathematics, Springer-Verlag, New York-Heidelberg, 1976.Google Scholar
[14] L., Auslander, E., Feig, and S., Winograd, New algorithms for the multidimensional discrete Fourier transform, IEEE Trans. Acoust. Speech, Signal, Proc. ASSP-31 (2) (1984), no. 1, 388–403.Google Scholar
[15] L., Auslander and R., Tolimieri, Is computing with the finite Fourier transform pure or applied mathematics? Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 6, 847–897.Google Scholar
[16] J., Ax, Zeroes of polynomials over finite fields, Amer. J., Math. 86 (1964), 255–261.Google Scholar
[17] L., Bartholdi and W., Woess, Spectral computations on lamplighter groups andDiestel-Leader graphs, J. Fourier Anal. Appl. 11 (2005), no. 2, 175–202.Google Scholar
[18] R., Beals, On orders of subgroups in Abelian groups: an elementary solution of an exercise of Herstein, Amer. Math. Monthly 116 (2009), no. 10, 923–926.Google Scholar
[19] M.B., Bekka, P., de la Harpe, and A., Valette, Kazhdan's property (T). New Mathematical Monographs, 11. Cambridge University Press, 2008.Google Scholar
[20] B.C., Berndt, R.J., Evans, and K.S., Williams, Gauss and Jacobi sums. Canadian Mathematical Society Series of Monographs and Advanced Texts. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1998.Google Scholar
[21] K.P., Bogart, An obvious proof of Burnside's lemma, Amer. Math. Monthly 98 (1991), no. 10, 927–928.Google Scholar
[22] W.L., Briggs and V.E., Henson, The DFT. An owner's manual for the discrete Fourier transform. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1995.Google Scholar
[23] D., Bump, Lie groups. Graduate Texts in Mathematics, 225. Springer-Verlag, New York, 2004.Google Scholar
[24] D., Bump, P., Diaconis, A., Hicks, L., Miclo, and H., Widom, An Exercise(?) in Fourier Analysis on the Heisenberg Group, Ann. Fac. Sci. Toulouse Math. (6) 26 (2017), no. 2, 263– 288.Google Scholar
[25] D., Bump and D., Ginzburg, Generalized Frobenius-Schur numbers, J. Algebra 278 (2004), no. 1, 294–313.Google Scholar
[26] P., Buser, Uber eine Ungleichung von Cheeger, Math. Z. 158 (1978), no. 3, 245–252.Google Scholar
[27] P., Buser, A note on the isoperimetric constant, Ann. Sci. Ecole Norm. Sup. (4) 15 (1982), no. 2, 213–230.Google Scholar
[28] T., Ceccherini-Silberstein, F., Scarabotti, and F., Tolli, Trees, wreath products and finite Gelfand pairs, Adv. Math. 206 (2006), no. 2, 503–537.Google Scholar
[29] T., Ceccherini-Silberstein, F., Scarabotti, and F., Tolli, Harmonic analysis on finite groups: representation theory, Gelfand pairs and Markov chains. Cambridge Studies in Advanced Mathematics 108, Cambridge University Press, 2008.Google Scholar
[30] T., Ceccherini-Silberstein, A., Machi, F., Scarabotti, and F., Tolli, Induced representation and Mackey theory, J. Math. Sci. (New York) 156 (2009), no. 1, 11–28.Google Scholar
[31] T., Ceccherini-Silberstein, F., Scarabotti, and F., Tolli, Clifford theory and applications, J. Math. Sci. (New York) 156 (2009), no. 1, 29–43.Google Scholar
[32] T., Ceccherini-Silberstein, F., Scarabotti, and F., Tolli, Representation theory of wreath products of finite groups, J. Math. Sci. (New York) 156 (2009), no. 1, 44–55.Google Scholar
[33] T., Ceccherini-Silberstein, F., Scarabotti, and F., Tolli, Representation theory of the symmetric groups: the Okounkov-Vershik approach, character formulas, and partition algebras. Cambridge Studies in Advanced Mathematics 121, Cambridge University Press, 2010.Google Scholar
[34] T., Ceccherini-Silberstein, F., Scarabotti, and F., Tolli, Representation theory and harmonic analysis of wreath products of finite groups. London Mathematical Society Lecture Note Series 410, Cambridge University Press, 2014.Google Scholar
[35] T., Ceccherini-Silberstein, F., Scarabotti, and F., Tolli, Mackey's theory of τ -conjugate representations for finite groups, Jpn. J. Math. 10 (2015), no. 1, 43–96.Google Scholar
[36] T., Ceccherini-Silberstein, F., Scarabotti, and F., Tolli, Mackey's criterion for subgroup restriction of Kronecker products and harmonic analysis on Clifford groups, Tohoku Math. J. (2) 67 (2015), no. 4, 553–571.Google Scholar
[37] T., Ceccherini-Silberstein, F., Scarabotti, and F., Tolli, Harmonic analysis and spherical functions for multiplicity-free induced representations. In preparation.
[38] J., Cheeger, A lower bound for the smallest eigenvalue of the Laplacian. In Problems in analysis (Papers dedicated to Salomon Bochner, 1969), pp. 195–199. Princeton Univ. Press, 1970.Google Scholar
[39] C., Chevalley, Demonstration d'une hypothese de M., Artin, Abh. Math. Sem. Univ. Hamburg 11 (1935), no. 1, 73–75.Google Scholar
[40] P., Chiu, Cubic Ramanujan graphs, Combinatorica 12 (1992), no. 3, 275–285.Google Scholar
[41] J.W., Cooley and J.W., Tukey, An algorithm for the machine calculation of complex Fourier series, Math. Comp. 19 (1965), 297–301.Google Scholar
[42] Ch.W., Curtis and I., Reiner, Representation theory of finite groups and associative algebras. Reprint of the 1962 original.Wiley Classics Library. A Wiley-Interscience Publication. John Wiley & SonsInc., , New York, 1988.Google Scholar
[43] Ch.W., Curtis and I., Reiner, Methods of representation theory. With applications to finite groups and orders. Voll. I and II. Pure and Applied Mathematics (New York). A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1981 and 1987.Google Scholar
[44] D., D'Angeli and A., Donno, Crested products of Markov chains, Ann. Appl. Probab. 19 (2009), no. 1, 414–453.Google Scholar
[45] D., D'Angeli and A., Donno, Wreath product of matrices, Linear Algebra Appl. 513 (2017), 276–303.Google Scholar
[46] D., D'Angeli and A., Donno, Shuffling matrices, Kronecker product and Discrete Fourier Transform, Discrete Appl. Math. 233 (2017), 1–18.Google Scholar
[47] H., Davenport, The higher arithmetic. An introduction to the theory of numbers. Eighth edition. With editing and additional material by James H. Davenport. Cambridge University Press, Cambridge, 2008.Google Scholar
[48] H., Davenport and H., Hasse, Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fallen, J. Reine Angew. Math. 172 (1935), 151–182.Google Scholar
[49] G., Davidoff, P., Sarnak, and A., Valette, Elementary number theory, group theory, and Ramanujan graphs. London Mathematical Society Student Texts, 55. Cambridge University Press, Cambridge, 2003.Google Scholar
[50] M., Davio, Kronecker products and shuffle algebra, IEEE Trans. Comput. 30 (1981), no. 2, 116–125.Google Scholar
[51] Ph.J., Davis, Circulant matrices, Pure and Applied Mathematics. John Wiley & Sons, New York-Chichester-Brisbane, 1979.Google Scholar
[52] P., Deligne, La conjecture de Weil. I, Inst. Hautes Etudes Sci. Publ. Math. 43 (1974), 273– 307.Google Scholar
[53] P., Diaconis, Group representations in probability and statistics. Institute of Mathematical Statistics Lecture Notes—Monograph Series, 11. Institute of Mathematical Statistics, Hayward, CA, 1988.Google Scholar
[54] P., Diaconis and D., Rockmore, Efficient computation of the Fourier transform on finite groups, J. Amer. Math. Soc. 3 (1990), no. 2, 297–332.Google Scholar
[55] B.W., Dickinson and K., Steiglitz, Eigenvectors and functions of the discrete Fourier transform, IEEE Trans. Acoust. Speech Signal Process. 30 (1982), no. 1, 25–31.Google Scholar
[56] I., Dinur, The PCP theorem by gap amplification, Journal of the ACM, 54 (2007) No. 3, Art. 12, 44 p.Google Scholar
[57] J., Dodziuk, Difference equations, isoperimetric inequality and transience of certain random walks, Trans. Amer. Math. Soc. 284 (1984), no. 2, 787–794.Google Scholar
[58] A., Donno, Replacement and zig-zag products, Cayley graphs and Lamplighter randomwalk, Int. J. Group Theory 2 (2013), no. 1, 11–35.Google Scholar
[59] A., Donno, Generalized wreath products of graphs and groups, Graphs Combin. 31 (2015), no. 4, 915–926.Google Scholar
[60] P., Erdős, Uber die Reihe, Mathematica, Zutphen B 7 (1938), 1–2.Google Scholar
[61] W., Feller, An introduction to probability theory and its applications. Vol. II. Second edition John Wiley & Sons, Inc., New York-London-Sydney 1971.Google Scholar
[62] G.B., Folland, Harmonic analysis in phase space. Annals of Mathematics Studies, 122. Princeton University Press, 1989.Google Scholar
[63] W., Fulton and J., Harris, Representation Theory. A first course. Springer-Verlag, New York, 1991.Google Scholar
[64] O., Gabber and Z., Galil, Explicit constructions of linear-sized superconcentrators. Special issued dedicated to Michael Machtey. J. Comput. System Sci. 22 (1981), no. 3, 407– 420.Google Scholar
[65] C., Godsil and G., Royle, Algebraic graph theory. Graduate Texts in Mathematics, 207. Springer-Verlag, New York, 2001.Google Scholar
[66] I.J., Good, The interaction algorithm and practical Fourier analysis, J. Roy. Statist. Soc. Ser. B 20 (1958), 361–372.Google Scholar
[67] B., Green and T., Tao, The primes contain arbitrarily long arithmetic progressions, Ann. of Math. 167 (2008), no. 2, 481–547.Google Scholar
[68] R.E., Greenwood and A.M., Gleason, Combinatorial relations and chromatic graphs, Canad. J. Math. 7 (1955), 1–7.Google Scholar
[69] R.I., Grigorchuk, P.-H., Leemann, and T., Nagnibeda, Lamplighter groups, de Brujin graphs, spider-web graphs and their spectra, J. Phys. A 49 (2016), no. 20, 205004, 35 p.Google Scholar
[70] R.I., Grigorchuk and A., Zuk, The lamplighter group as a group generated by a 2-state automaton, and its spectrum, Geom. Dedicata 87 (2001), no. 1–3, 209–244.Google Scholar
[71] I.N., Herstein, Topics in algebra. Second edition. Xerox College Publishing, Lexington, Mass.-Toronto, Ont., 1975.Google Scholar
[72] Ch.J. Hillar and D.L., Rhea, Automorphisms of finite Abelian groups, Amer. Math. Monthly 114 (2007), no. 10, 917–923.Google Scholar
[73] D.A., Holton and J., Sheehan, The Petersen graph. Australian Mathematical Society Lecture Series, 7. Cambridge University Press, Cambridge, 1993.Google Scholar
[74] Sh. Hoory, N., Linial, and A., Wigderson, Expander graphs and their applications, Bull. Amer. Math. Soc. (N.S.) 43 (2006), no. 4, 439–561.Google Scholar
[75] R.A., Horn and R.Ch.|Johnson, Matrix analysis. Second edition. Cambridge University Press, Cambridge, 2013.Google Scholar
[76] R., Howe, On the role of the Heisenberg group in harmonic analysis, Bull. Amer. Math. Soc. (N.S.) 3 (1980), no. 2, 821–843.Google Scholar
[77] L.K., Hua and H.S., Vandiver, Characters over certain types of rings with applications to the theory of equations in a finite field, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 94–99.Google Scholar
[78] B., Huppert, Character theory of finite groups. De Gruyter Expositions in Mathematics, 25, Walter de Gruyter, 1998.Google Scholar
[79] K., Ireland and M., Rosen, A classical introduction to modern number theory. Second edition. Graduate Texts in Mathematics, 84. Springer-Verlag, New York, 1990.Google Scholar
[80] I.M., Isaacs, Character theory of finite groups. Corrected reprint of the 1976 original [Academic Press, New York]. Dover PublicationsInc., , New York, 1994.Google Scholar
[81] H., Iwaniec and E., Kowalski, Analytic number theory. American Mathematical Society Colloquium Publications, 53. American Mathematical Society, Providence, RI, 2004.Google Scholar
[82] G.D., James and A., Kerber, The representation theory of the symmetric group. Encyclopedia of Mathematics and its Applications, 16, Addison-Wesley, Reading, MA, 1981.Google Scholar
[83] S., Jimbo and A., Maruoka, Expanders obtained from affine transformations, Combinatorica 7 (1987), no. 4, 343–355.Google Scholar
[84] S., Karlin and H.M., Taylor, An introduction to stochastic modeling. Third edition. Academic Press Inc., , San Diego, CA, 1998.Google Scholar
[85] Y., Katznelson, An introduction to harmonic analysis. Third edition. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 2004.Google Scholar
[86] S.P., Khekalo, The Bessel function over finite fields, Integral Transforms Spec. Funct. 16 (2005), no. 3, 241–253.Google Scholar
[87] A.W., Knapp, Basic algebra. Cornerstones. Birkhauser BostonInc., , Boston, MA, 2006.Google Scholar
[88] A.W., Knapp, Advanced algebra. Cornerstones. Birkhauser BostonInc., , Boston, MA, 2007.Google Scholar
[89] A., Kurosh, Higher algebra. Translated from the Russian by George Yankovsky. Reprint of the 1972 translation. “Mir,” Moscow, 1988.Google Scholar
[90] H., Kurzweil and B., Stellmacher, The theory of finite groups. An introduction. Translated from the 1998 German original. Universitext. Springer-Verlag, New York, 2004.Google Scholar
[91] P., Lancaster and M., Tismenetsky, The theory of matrices. Second edition. Computer Science and Applied Mathematics. Academic Press, Inc., Orlando, FL, 1985.Google Scholar
[92] S., Lang, SL2(R). Reprint of the 1975 edition. Graduate Texts inMathematics, 105. Springer-Verlag, New York, 1985.Google Scholar
[93] S., Lang, Algebra. Revised third edition. Graduate Texts in Mathematics, 211. Springer-Verlag, New York, 2002.Google Scholar
[94] F., Lehner, M., Neuhauser, and W., Woess, On the spectrum of lamplighter groups and percolation clusters, Math. Ann. 342 (2008), no. 1, 69–89.Google Scholar
[95] W.C.W., Li, Number theory with applications. Series on University Mathematics, 7. World Scientific Publishing Co.Inc., , River Edge, NJ, 1996.Google Scholar
[96] R., Lidl and H., Niederreiter, Finite fields. With a foreword by P.M., Cohn. Second edition. Encyclopedia of Mathematics and its Applications, 20. Cambridge University Press, Cambridge, 1997.Google Scholar
[97] J.H., van Lint and R.M.Wilson, A course in combinatorics. Second edition. Cambridge University Press, Cambridge, 2001.Google Scholar
[98] L.H., Loomis, An introduction to abstract harmonic analysis. D. Van Nostrand CompanyInc., , Toronto-New York-London, 1953.Google Scholar
[99] A., Lubotzky, Discrete groups, expanding graphs and invariant measures. With an appendix by Jonathan D., Rogawski. Progress in Mathematics, 125. Birkh Auser Verlag, Basel, 1994.Google Scholar
[100] A., Lubotzky, Expander graphs in pure and applied mathematics, Bull. Amer. Math. Soc. (N.S.) 49 (2012), no. 1, 113–162.Google Scholar
[101] A., Lubotzky, R., Phillips, and P., Sarnak, Ramanujan graphs, Combinatorica 8 (1988), no. 3, 261–277.Google Scholar
[102] A., Machi, Teoria dei gruppi. Milano, Feltrinelli, 1974.Google Scholar
[103] A., Machi, Groups. An introduction to ideas and methods of the theory of groups. Unitext, 58. Springer, Milan, 2012.Google Scholar
[104] J.H., MacClellan and T.W., Parks, Eigenvalue and eigenvector decomposition of the discrete Fourier transform, IEEE Trans. Audio Electroacoust. AU-20 (1972), no. 1, 66–74.Google Scholar
[105] I.G., Macdonald, Symmetric functions and Hall polynomials. Second edition. With contributions by A., Zelevinsky. Oxford Mathematical Monographs. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1995.Google Scholar
[106] J.H., MacKay, Another proof of Cauchy's group theorem, Amer. Math. Monthly 66 (1959), 119.Google Scholar
[107] G.W., Mackey, Unitary representations of group extensions. I, Acta Math. 99 (1958), 265– 311.Google Scholar
[108] G.W., Mackey, Unitary group representations in physics, probability, and number theory, Second edition. Advanced Book Classics. Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, 1989.Google Scholar
[109] A.W.Marcus, D.A., Spielman, and N., Srivastava, Interlacing families I: Bipartite Ramanujan graphs of all degrees, Ann. of Math. (2) 182 (2015), no. 1, 307–325.Google Scholar
[110] A.W., Marcus, D.A., Spielman, and N., Srivastava, Interlacing families IV: Bipartite Ramanujan graphs of all sizes. 2015 IEEE 56th Annual Symposium on Foundations of Computer Science–FOCS 2015, 1358–1377, IEEE Computer Soc., Los Alamitos, CA, 2015.Google Scholar
[111] G.A., Margulis, Explicit constructions of expanders, Problemy Peredachi Informatsii 9 (1973), no. 4, 71–80.Google Scholar
[112] G.A., Margulis, Explicit group-theoretic constructions of combinatorial schemes and their applications in the construction of expanders and concentrators, Problemy Peredachi Informatsii 24 (1988), no. 1, 51–60.Google Scholar
[113] S., Mac Lane and G., Birkhoff, Algebra. Third edition. Chelsea Publishing Co., New York, 1988.Google Scholar
[114] A.I., Mal'cev, Foundations of linear algebra. Translated from the Russian by Thomas Craig, Brown. San Francisco, Calif.-London, 1963.Google Scholar
[115] A.I., Markushevich, The theory of analytic functions: a brief course. Translated from the Russian by Eugene, Yankovsky. “Mir,” Moscow, 1983.Google Scholar
[116] M., Morgenstern, Ramanujan diagrams, SIAM J. Discrete Math. 7 (1994), no. 4, 560–570.Google Scholar
[117] T., Nagell, Introduction to number theory. Second edition. Chelsea Publishing Co., New York 1964.Google Scholar
[118] M., Nathanson, Elementary methods in number theory. Graduate Texts in Mathematics, Vol. 195, Springer-Verlag, New York, 2000.Google Scholar
[119] M.A., Naimark and A.I., Stern, Theory of group representations. Springer-Verlag, New York, 1982.Google Scholar
[120] G., Navarro, On the fundamental theorem of finite abelian groups, Amer. Math. Monthly 110 (2003), no. 2, 153–154.Google Scholar
[121] P.M., Neumann, A lemma that is not Burnside's, Math. Sci. 4 (1979), no. 2, 133–141.Google Scholar
[122] A., Nilli, Tight estimates for eigenvalues of regular graphs, Electron. J. Combin. 11 (2004), no. 1, Note 9, 4 p.Google Scholar
[123] I., Piatetski-Shapiro, Complex representations of GL(2, K) for finite fields K. Contemporary Mathematics, 16. American Mathematical Society, Providence, R.I., 1983.Google Scholar
[124] C., Procesi, Lie groups. An approach through invariants and representations. Universitext. Springer, New York, 2007.Google Scholar
[125] Ch.M., Rader, Discrete Fourier transforms when the number of data samples is prime, Proc. IEEE 56 (1968), 1107–1108.Google Scholar
[126] O., Reingold, Undirected connectivity in log-space, Journal of the ACM, 55 (2008), no. 4, Art. 17, 24 p.Google Scholar
[127] O., Reingold, L., Trevisan, and S., Vadhan, Pseudorandom walks on regular digraphs and the RL vs. L problem. STOC' 06: Proceedings of the 38th Annual ACM Symposium on Theory of Computing, 457–466, ACM, New York, 2006.Google Scholar
[128] O., Reingold, S., Vadhan, and A., Wigderson, Entropy waves, the zig-zag graph product, and new constant-degree expanders, Ann. of Math. (2) 155 (2002), no. 1, 157–187.Google Scholar
[129] D.J.S., Robinson, A course in the theory of groups. Second edition. Graduate Texts in Mathematics, 80. Springer-Verlag, New York, 1996.Google Scholar
[130] D.J., Rose, Matrix identities of the fast Fourier transform, Linear Algebra Appl. 29 (1980), 423–443.Google Scholar
[131] K.F., Roth, On certain sets of integers, J. London Math. Soc. 28 (1953), 104–109.Google Scholar
[132] J.J., Rotman, An introduction to the theory of groups. Fourth edition. Graduate Texts in Mathematics, 148. Springer-Verlag, New York, 1995.Google Scholar
[133] W., Rudin, Real and complex analysis. Third edition. McGraw-Hill Book Co., New York, 1987.Google Scholar
[134] W., Rudin, Fourier analysis on groups. Reprint of the 1962 original.Wiley Classics Library. A Wiley-Interscience Publication. John Wiley & SonsInc., , New York, 1990.Google Scholar
[135] P., Sarnak, Some applications of modular forms. Cambridge Tracts in Mathematics, 99, Cambridge University Press, Cambridge, 1990.Google Scholar
[136] F., Scarabotti and F., Tolli, Harmonic analysis of finite lamplighter random walks, J. Dyn. Control Syst. 14 (2008), no. 2, 251–282.Google Scholar
[137] F., Scarabotti and F., Tolli, Harmonic analysis on a finite homogeneous space, Proc. Lond. Math. Soc. (3) 100 (2010), no. 2, 348–376.Google Scholar
[138] F., Scarabotti and F., Tolli, Harmonic analysis on a finite homogeneous space II: the Gelfand- Tsetlin decomposition, Forum Math. 22 (2010), no. 5, 879–911.Google Scholar
[139] F., Scarabotti and F., Tolli, Hecke algebras and harmonic analysis on finite groups, Rend. Mat. Appl. (7) 33 (2013), no. 1–2, 27–51.Google Scholar
[140] F., Scarabotti and F., Tolli, Induced representations and harmonic analysis on finite groups, Monatsh. Math. 181 (2016), no. 4, 937–965.Google Scholar
[141] M., Scafati and G., Tallini, Geometria di Galois e teoria dei codici. Ed. CISU 1995.
[142] J., Schulte, Harmonic analysis on finite Heisenberg groups, European J. Combin. 25 (2004), no. 3, 327–338.Google Scholar
[143] A., Selberg, An elementary proof of Dirichlet's theorem about primes in an arithmetic progression, Ann. of Math. (2) 50 (1949), 297–304.Google Scholar
[144] J.P., Serre, A course in arithmetic. Translated from the French. Graduate Texts in Mathematics, No. 7. Springer-Verlag, New York-Heidelberg, 1973.
[145] J.P., Serre, Linear representations of finite groups. Graduate Texts in Mathematics, Vol. 42. Springer-Verlag, New York-Heidelberg, 1977.Google Scholar
[146] J.P., Serre, Repartition asymptotique des valeurs propres de l'operateur de Hecke Tp, J. Amer. Math. Soc. 10 (1997), no. 1, 75–102.Google Scholar
[147] R., Shaw, Linear algebra and group representations. Vol. II. Multilinear algebra and group representations. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London- New York, 1983.Google Scholar
[148] B., Simon, Representations of finite and compact groups. American Math. Soc., 1996.Google Scholar
[149] R.P., Stanley, Enumerative combinatorics, Vol.1. Cambridge University Press, 1997.
[150] E.M., Stein and R., Shakarchi, Fourier analysis. An introduction. Princeton Lectures in Analysis, 1. Princeton University Press, 2003.Google Scholar
[151] E.M., Stein and R., Shakarchi, Complex analysis. Princeton Lectures in Analysis, 2. Princeton University Press, 2003.Google Scholar
[152] J.R., Stembridge, On Schur's Q-functions and the primitive idempotents of a commutative Hecke algebra, J. Algebraic Combin. 1 (1992), no. 1, 71–95.Google Scholar
[153] C., Stephanos, Sur une extension du calcul des substitutions lineaires, Journal de Mathm´ atiques Pures et Appliquees V, 6 (1900), 73–128.Google Scholar
[154] S., Sternberg, Group theory and physics. Cambridge University Press, Cambridge, 1994.Google Scholar
[155] E., Szemeredi, On sets of integers containing no four elements in arithmetic progression, Acta Math. Acad. Sci. Hungar. 20 (1969), 89–104.Google Scholar
[156] E., Szemeredi, On sets of integers containing no k elements in arithmetic progression, Acta Arith. 27 (1975), 199–245.Google Scholar
[157] T., Tao, An uncertainty principle for cyclic groups of prime order, Math. Res. Lett. 12 (2005), no. 1, 121–127.Google Scholar
[158] T., Tao, The ergodic and combinatorial approaches to Szemeredi's theorem. Additive combinatorics, 145–193, CRM Proc. Lecture Notes, 43, Amer. Math. Soc., Providence, RI, 2007.Google Scholar
[159] A., Terras, Fourier analysis on finite groups and applications. London Mathematical Society Student Texts, 43. Cambridge University Press, Cambridge, 1999.Google Scholar
[160] R., Tolimieri, M., An, and C., Lu, Mathematics of multidimensional Fourier transform algorithms. Second edition. Signal Processing and Digital Filtering. Springer-Verlag, New York, 1997.Google Scholar
[161] A., Valette, Graphes de Ramanujan et applications. Seminaire Bourbaki, Vol. 1996/97. Asterisque No. 245 (1997), Exp. No. 829, 4, 247–276.Google Scholar
[162] E., Vallejo, A diagrammatic approach to Kronecker squares, J. Combin. Theory Ser. A 127 (2014), 243–285.Google Scholar
[163] Ch.F., Van Loan, Computational frameworks for the fast Fourier transform. Frontiers in Applied Mathematics, 10. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992.Google Scholar
[164] E., Warning, Bemerkung zur vorstehenden Arbeit, Abh. Math. Sem. Univ. Hamburg 11 (1935), no. 1, 76–83.Google Scholar
[165] A., Weil, Numbers of solutions of equations in finite fields, Bull. Amer.Math. Soc. 55 (1949), 497–508.Google Scholar
[166] H., Weyl, Algebraic theory of numbers. Annals of Mathematics Studies, no. 1. Princeton University Press, 1940.Google Scholar
[167] H., Wielandt, Finite permutation groups. Academic Press, New York-London, 1964.Google Scholar
[168] S., Winograd, On computing the discrete Fourier transform, Math. Comp. 32 (1978), no. 141, 175–199.Google Scholar
[169] E.M., Wright, Burnside's lemma: a historical note, J. Combin. Theory Ser. B 30 (1981), no. 1, 89–90.Google Scholar
[170] G., Zappa, Fondamenti di teoria dei gruppi, Vol. I. Consiglio Nazionale delle RicercheMonografie Matematiche, 13 Edizioni Cremonese, Rome, 1965.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
×