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Multiply Harmonic Functions

Published online by Cambridge University Press:  22 January 2016

Kohur Gowrisankaran
Kohur Gowrisankaran*
Affiliation:
Tata Institute of Fundamental Research, Bombay
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Let Ω and Ω′ be two locally compact, connected Hausdorff spaces having countable bases. On each of the spaces is defined a system of harmonic functions satisfying the axioms of M. Brelot [2]. The following is the description of such a system. To each open set of Ω is assigned a vector space of finite continuous functions, called the harmonic functions, on this set.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 28 , October 1966 , pp. 27 - 48
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Bourbaki, N., Intégration Ch. 5, Intégration des mesures.Google Scholar
[2] Brelot, M., Lectures on Potential Theory, T.I.F.R., 1960.Google Scholar
[3] Brelot, M., Séminaire de Théorie du potentiel II (1958).Google Scholar
[4] Choquet, G., Séminaire Bourbaki 130, Dec. 1956.Google Scholar
[5] Gowrisankaran, K., Ann. Inst. Fourier 13, 2 (1963), p. 307–356.CrossRefGoogle Scholar
[6] Hervé, R. M., Ann. Inst. Fourier 12 (1962), p. 415–571.CrossRefGoogle Scholar