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Characterizations of Supports of Balayaged Measures

Published online by Cambridge University Press:  22 January 2016

Masayuki Itô
Masayuki Itô*
Affiliation:
Mathematical Institute, Nagoya University
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Beurling and Deny [1], [2] introduced Dirichlet spaces by generalizing the notion of “energy” in potential theory. They showed the existences of balayaged measures and condensor measures in the theory of Dirichlet spaces. The purpose of this paper is to characterize the supports of those measures. First we obtain the following result.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 28 , October 1966 , pp. 203 - 230
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Beurling, A. and Deny, J.: Espaces de Dirichlet I, Le cas élémentaire, Acta Math., 99 (1958), 103–124.Google Scholar
[2] Beurling, A. and Deny, J.: Dirichlet spaces, proc. Nat. Acad. Sc. U.S.A., 45 (1959), 208–215.Google Scholar
[3] Bochner, S.: Harmonic analysis and the theory of probablity, Berkeley, 1955.Google Scholar
[4] Deny, J.: Sur les espaces de Dirichlet, Sem. théorie du potentiel, Paris, 1957.Google Scholar
[5] Deny, J.: Principe complet du maximum et contractions, Colloque Intesrnational du C.N.R.S., 1964.Google Scholar
[6] Schwartz, L.: Théorie des distributions II, Paris, 1951.Google Scholar