Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T23:54:42.957Z Has data issue: false hasContentIssue false
  • English
  • Français

Condensor Principle and the Unit Contraction

Published online by Cambridge University Press:  22 January 2016

Masayuki Itô
Masayuki Itô*
Affiliation:
Mathematical Institute Nagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
[2] Beurling, A. & Deny, J.: Dirichlet spaces, Proc. Nat. Acad. Sc. U.S.A., 45 (1959), 208–215.Google Scholar
[3] Deny, J.: Sur les espaces de Dirichlet, Sémin. théorie du potentiel, Paris, 1957.Google Scholar
[4] Deny, J.: Principe complet de mixamum et Contractions, Ann. Inst. Fourier, 15 (1965), 259–272.CrossRefGoogle Scholar
[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