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On Principal Function Problem

Published online by Cambridge University Press:  22 January 2016

Mitsuru Nakai
Mitsuru Nakai*
Affiliation:
Mathematical Institute, Nagoya University, Nagoya, Japan
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Sario’s theory of principal functions fully discussed in his research monograph [3] with Rodin stems from the principal function problem which is to find a harmonic function p on an open Riemann surface R imitating the ideal boundary behavior of the given harmonic function s in a neighborhood A of the ideal boundary δ of R.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 38 , March 1970 , pp. 85 - 90
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Ahlfors-L. Sario, L.: Riemann surfaces, Princeton Univ. Press, Princeton, N.J., 1960.CrossRefGoogle Scholar
[2] Nakai, M.: Principal function problem on harmonic spaces, Lecture Abstract for Function Theory branch of May Meeting of Math. Soc. Japan, 1968 (in Japanese).Google Scholar
[3] Rodin-L. Sario, B.: Principal Functions, Van Nostrand, Princeton, N.J., 1967.Google Scholar
[4] Sario, L.: A linear operator method on arbitrary Riemann surfaces, Trans. Amer. Math. Soc., 72 (1952), 281–295.CrossRefGoogle Scholar
[5] Yamaguchi, H.: Regular operators and spaces of harmonic functions with finite Dirichlet integral on open Riemann surfaces, J. Math. Kyoto Univ., 8 (1968), 169–198.Google Scholar
[6] Yosida, K.: Functional Analysis, Springer-Verlag, Berlin-GBttingen-Heidelberg, 1965.Google Scholar