Abstract
An analog of the Nehari theorem for character-automorphic functions with respect to the action of Fuchsian groups of Widom-Carleson type is proved. A solvability criteria for the Nevanlinna-Pick problem in a Denjoy domain with homogeneous boundary is given as an example.
This work was supported by the ISF Grant no U2Z000
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References
Abrahamse M., The Pick interpolation theorem for finitely connected domains, Michigan Math. J. 26 (1979) 195–203.
Ball J., A lifting theorem for operator models of finite rank on multiply-connected domains, J. Operator Theory 1 (1979), 3–25.
Ball J. and Vinnikov V., Zero-pole interpolation for matrix meromorphic functions on an algebraic curve with determinantal representation, Acta Math. Applicandae (to appear).
Jones P. and Marshall D., Critical points of Green’s function, harmonic measure, and the corona problem, Arkiv för Matematik 23 (1985) 281–314.
Hasumi M., Hardy Classes on Infinitely Connected Riemann Surfaces, Lecture Notes in Math. 1027, Springer Verlag, Berlin and New York, 1983.
Heins M., On an example of Donald Marshall concerning automorphic Pick-Nevanlinna interpolation problems Complex Variables Theory Appl. 7 (1986) 71–78.
Krein M.G. and Nudelman A.A., Markov Moment Problem and Extremal Problems, Nauka, Moscow, 1973 ( Russian).
Livsic M., Kravitsky N., Markus A., Vinnikov V., Commuting Nonselfadjoint Operators and their Applications to System Theory, Kluwer, 1995
Nikolskii N.K., Treatise on the Shift Operator, Springer Verlag. Berlin and New York, 1986.
Pavlov B. and Fedorov S., The group of shifts and harmonic analysis on a Riemann surface of genus one, Algebra i Analiz 1 (1989) 132–168, (Russian).
Pommerenke Ch., On the Green’s function of Fuchsian groups, Ann. Acad. Sci. Fenn. 2 (1976) 409–427.
Samokhin M., Some classical problems in the theory of analytic functions in domains of Parreau-Widom type, Math. USSR Sbornik 73 (1992) 273–288.
Sodin M.L. and Yuditskii P.M., Infinite-dimensional Jacobi inversion problem, almost-periodic Jacobi matrices with homogeneous spectrum, and Hardy classes of character-automorphic functions, Journ. of Geometr. Analysis (to appear).
Widom H., H p sections of vector bundles over Riemann surfaces, Ann. of Math. 94 (1971) 304–323.
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Kupin, S., Yuditskii, P. (1997). Analogs of the Nehari and Sarason theorems for character-automorphic functions and some related questions. In: Dym, H., Katsnelson, V., Fritzsche, B., Kirstein, B. (eds) Topics in Interpolation Theory. Operator Theory Advances and Applications, vol 95. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8944-5_17
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DOI: https://doi.org/10.1007/978-3-0348-8944-5_17
Publisher Name: Birkhäuser, Basel
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