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Mittag-Leffler Theorems on Riemann Surfaces and Riemannian Manifolds
Published online by Cambridge University Press: 20 November 2018
Abstract
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Cauchy and Poisson integrals over unbounded sets are employed to prove Mittag-Leffler type theorems with massive singularities as well as approximation theorems for holomorphic and harmonic functions.
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- Copyright © Canadian Mathematical Society 1998
References
1.
Aronszajn, N., Sur les décompositions des fonctions analytiques uniformes et sur leur applications. Acta Math.
65(1935), 1–156.Google Scholar
2.
Bagby, T. and Blanchet, P., Uniform approximation on Riemannian manifolds. J.Analyse Math.
62(1994), 47–76.Google Scholar
4.
Boivin, A., Carleman approximation on Riemann surfaces. Math. Ann.
275(1986), 57–70.Google Scholar
5.
Browder, F.E., Functional analysis and partial differential equations II. Math. Ann.
145(1962), 81–226.Google Scholar
6.
Chavel, I., Riemannian Geometry: A Modern Introduction. 1993, Cambridge Univ. Press.Google Scholar
7.
Deutsch, F., Simultaneous interpolation and approximation in topological linear spaces. SIAM J. Appl. Math.
14(1966), 1180–1190.Google Scholar
10.
Gauthier, P.M., Meromorphic uniform approximation on closed subsets of open Riemann surfaces. In: Approximation Theory and Functional Analysis, 1979, (ed. Prolla, J.B.), North-Holland, 139–158.Google Scholar
11.
Gauthier, P.M.,Goldstein, M. and Ow, W.H., Uniform approximation on closed sets by harmonic functions with Newtonian singularities. J. London Math. Soc. (2)
28(1983), 71–82.Google Scholar
12.
Gauthier, P.M. and Hengartner, W., Approximation Uniforme Qualitative sur des Ensembles Non-bornés. 1982, Presses Univ. Montrèal.Google Scholar
13.
Gauthier, P.M. and Tarkhanov, N.N., Degenerate cases of uniform approximation by solutions of systems with surjective symbols. Canad. J. Math.
45(1993), 740–757.Google Scholar
14.
Gunning, R.C. and Narasimhan, R., Immersion of open Riemann surfaces. Math. Ann.
174(1967), 103–108.Google Scholar
15.
Havin, V.P., Separation of singularities of analytic functions. Dokl. Akad. Nauk USSR
121(1958), 239–242.Google Scholar
16.
Lehner, J., Discontinuous Groups and Automorphic Functions. 1964, Amer. Math. Soc.Google Scholar
17.
Magnus, R.J., The spectrum and eigenspaces of a meromorphic operator-valued function. Proc. Royal Soc. Edinburgh
127(1997), 1027–1051.Google Scholar
20.
Saakian, R. Sh., Some applications of theorems on approximation by an analytic function. Izv. Akad. Nauk Armyan. SSR Ser. Mat. 24(1989), 259–268. English translation, Soviet J. Contemporary Math. Anal.
24(1989), 51–55.Google Scholar
21.
Schulze, B.-W. and Wildenhain, G., Methoden der Potentialtheorie für elliptische Differentialgleichungen beliebiger Ordnung. 1977, Akademie-Verlag.Google Scholar
23.
Tarkhanov, N.N., Ryad Lorana dlya reshenii ellipticheskikh sistem. 1991, Nauka, Novosibirsk; English translation, The Analysis of Solutions of Elliptic Equations. 1997, Kluwer.Google Scholar
24.
Tarkhanov, N.N., Approximation on compact sets by solutions of systems with surjective symbols. Uspekhi Mat. Nauk; English translation, Russian Math. Surveys
48(1993), 103–145.Google Scholar
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