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On the theorem of Kishi for a continuous function-kernel

Published online by Cambridge University Press:  22 January 2016

Isao Higuchi  and
Masayuki Itô
Isao Higuchi
Affiliation:
Suzuka College of Technology and Nagoya University
Masayuki Itô
Affiliation:
Suzuka College of Technology and Nagoya University
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In the potential theory with respect to a non-symmetric function-kernel, the following theorem is obtained by M. Kishi ([3]).

Let X be a locally compact Hausdorff space and G be a lower semi-continuous function-kernel on X. Assume that G(x, x)>0 for any x in X and that G and the adjoint kernel Ğ of G satisfy “the continuity principle”.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 53 , May 1974 , pp. 127 - 135
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1974

References

[1] Durier, R.: Thèse, Faculté des Sciences d’Orsay, Université de Paris, 1969.Google Scholar
[2] Itô, M.: Sur les principes divers du maximum et le type positif, Nagoya Math. J., 44, 1971, p. 133–164.Google Scholar
[3] Kishi, M.: Maximum principles in the potential theory, Nagoya Math. J., 23, 1963, p. 165–187.Google Scholar
[4] Kishi, M.: An existence theorem in potential theory, Nagoya Math. J., 27, 1966, p. 133–137.Google Scholar