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The corona problem on finitely sheeted covering surfaces

Published online by Cambridge University Press:  22 January 2016

Mitsuru Nakai
Mitsuru Nakai*
Affiliation:
Department of Mathematics, Nagoya Institute of Technology, Gokiso, Showa, Nagoya 466, Japan
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The purpose of this paper is to show that the corona theorem is valid on any unbounded finitely sheeted covering surface if and only if the corona theorem is valid on its base surface.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 92 , December 1983 , pp. 163 - 173
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1983

References

[1] Ahlfors, L., Open Riemann surfaces and extremal problems on compact subregions, Comm. Math. Helv., 24 (1950), 100–134.CrossRefGoogle Scholar
[2] Behrens, M., The maximal ideal space of algebras of bounded analytic functions on infinitely connected domains, Trans. Amer. Math. Soc., 161 (1971), 359–380.CrossRefGoogle Scholar
[3] Carleson, L., Interpolation by bounded analytic functions and the corona problem, Ann. of Math., 76 (1962), 547–559.Google Scholar
[4] Gamelin, T., Localization of the corona problem, Pacific J. Math., 34 (1970), 73–81.CrossRefGoogle Scholar
[5] Gamelin, T., Uniform Algebras, Prentice-Hall, 1969.Google Scholar
[6] Gamelin, T., Uniform Algebras and Jensen Measures, London Math. Soc. Lecture Note Series, 32, 1978.Google Scholar
[7] Gamelin, T., Wolff’s proof of the corona theorem, Israel J. Math., 37 (1980), 113–119.CrossRefGoogle Scholar
[8] Hara, M., On Gamelin constants, NIT Seminar Note, 1981.Google Scholar
[9] Hara, M., The corona problem on 2-sheeted disks, Proc. Japan Acad., 58 (1982), 256–257.Google Scholar
[10] Nakai, M., Corona problem for Riemann surfaces of Parreau-Widom type, Pacific J. Math., 103 (1982), 103–109.Google Scholar
[11] Rudin, W., Real and Complex Analysis, McGraw-Hill, 1966.Google Scholar
[12] Segawa, S., Bounded analytic functions on unbounded covering surfaces, Pacific J. Math., 79 (1978), 183–187.CrossRefGoogle Scholar
[13] Selberg, H., Ein Satz über beschränkte endlichvieldeutige analytische Funktionen, Comm. Math. Helv., 9 (1937), 104–108.Google Scholar
[14] Stanton, C., Bounded analytic functions on a class of open Riemann surfaces, Pacific J. Math., 59 (1975), 557–565.CrossRefGoogle Scholar
[15] Stout, E., Two theorems concerning functions holomorphic on multiply connected domains, Bull. Amer. Math. Soc., 69 (1963), 527–530.CrossRefGoogle Scholar
[16] Widom, H., The maximum principle for multiple valued analytic functions, Acta Math., 126 (1971), 63–82.CrossRefGoogle Scholar
[17] Widom, H., Hp -sections of vector bundles over Riemann surfaces, Ann. of Math., 94 (1971), 304–324.CrossRefGoogle Scholar
[18] Yamamura, Y., On the existence of bounded analytic functions, Sci. Rep. Tokyo Kyoiku Daigaku, Sect. A, 10 (1969), 88–102.Google Scholar
[19] Zariski, O. and Samuel, P., Commutative Algebra, Vol. 1, Van Nostrand, 1958.Google Scholar