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Analytic Functions on Some Riemann Surfaces

Published online by Cambridge University Press:  22 January 2016

Nobushige Toda  and
Kikuji Matsumoto
Nobushige Toda
Affiliation:
Mathematical Institute, Nagoya University
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Some years ago, Kuramochi gave in his paper [5] a very interesting theorem, which can be stated as follows.

THEOREM OF KURAMOCHI. Let R be a hyperbolic Riemann surface of the class Of OHR(OHD,resp.). Then, for any compact subset K of R such that R—K is connected, R—K as an open Riemann surface belongs to the class 0AB(OAD resp.).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 22 , June 1963 , pp. 211 - 217
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1963

References

[1] Ahlfors, L. V. and Beurling, A.: Conformai invariants and function-theoretic null-sets, Acta Math., 83 (1950), 101–129.CrossRefGoogle Scholar
[2] Constantinescu, C. and Cornea, A.: Über den idealen Rand und einige seiner Anwendungen bei Klassifìkation der Riemannschen Fîächen, Nagoya Math. J., 13 (1958), 166–233.Google Scholar
[3] Constantinescu, C. and Cornea, A.: Über einige Problème von M. Heins, Rev. Math. pur. appl., 4 (1959), 277–281.Google Scholar
[4] Kametani, S.: On Hausdorff’s measures and generalized capacities with some of their applications to the theory of functions, Jap. J. Math., 19 (1945-48), 217–257.Google Scholar
[5] Kuramochi, Z.: On the behaviour of analytic functions on abstract Riemann surfaces, Osaka Math. J., 7 (1955), 109–127.Google Scholar
[6] Kuramochi, Z.: Representation of Riemann surfaces, Osaka Math. J., 11 (1959), 71–82.Google Scholar
[7] Kuroda, T.: On analytic functions on some Riemann surfaces, Nagoya Math. J., 10 (1956), 27–50.Google Scholar
[8] Kusunoki, Y. and Mori, S.: On the harmonic boundary of an open Riemann surface, II, Mem. Coll. Sci. Univ. Kyoto, 33 (1960), 209–223.Google Scholar
[9] Nakai, M.: A measure on the harmonic boundary of a Riemann surface, Nagoya Math. J., 17 (1960), 181–218.Google Scholar
[10] Noshiro, K.:Cluster Sets, Berlin (1960).Google Scholar