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Condensor Principle and the Unit Contraction

Published online by Cambridge University Press:  22 January 2016

Masayuki Itô
Masayuki Itô*
Affiliation:
Mathematical Institute Nagoya University
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Deny introduced in [4] the notion of functional spaces by generalizing Dirichlet spaces. In this paper, we shall give the following necessary and sufficient conditions for a functional space to be a real Dirichlet space.

Let be a regular functional space with respect to a locally compact Hausdorff space X and a positive measure ξ in X. The following four conditions are equivalent.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 30 , August 1967 , pp. 9 - 28
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Beurling, A. & Deny, J.: Espaces de Dirichlet, Le case élémentaire, Acta Math., 99 (1958), 103–124.Google Scholar
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[3] Deny, J.: Sur les espaces de Dirichlet, Sémin. théorie du potentiel, Paris, 1957.Google Scholar
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[5] Deny, J.: Les potentiel d’énergie finie. Acta Math., 82 (1950) 107–182.Google Scholar
[6] Itô, M.: Characterizations of supports of balayaged measures, Nagoya Math. J., 28 (1966), 203–230.Google Scholar
[7] Lion, G.: Principle complet du maximum et semi-groupes sous-markoviens, Sémin. théorie du potentiel, Paris, 1964.Google Scholar