Characterizations of Supports of Balayaged Measures

Masayuki Itô

doi:10.1017/S0027763000024053

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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.

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

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Itô, Masayuki 1967. Le principe de domination de Ninomiya pour les potentiels pris par rapport au noyau invariable de composition. Proceedings of the Japan Academy, Series A, Mathematical Sciences, Vol. 43, Issue. 8,

Itô, Masayuki 1967. A note on extended regular functional spaces. Proceedings of the Japan Academy, Series A, Mathematical Sciences, Vol. 43, Issue. 6,

Itô, Masayuki 1967. Condensor Principle and the Unit Contraction. Nagoya Mathematical Journal, Vol. 30, Issue. , p. 9.

Itô, Masayuki 1967. On Total Masses of Balayaged Measures. Nagoya Mathematical Journal, Vol. 30, Issue. , p. 263.

Itô, Masayuki 1968. The Singular Measure of a Dirichlet Space. Nagoya Mathematical Journal, Vol. 32, Issue. , p. 337.

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Kireitov, V. R. 1995. The cauchy problem, the dirichlet problem, and some inverse problems for the one-velocity Peierls equation of the theory of radiation transport in a homogeneously absorbing and scattering medium with isotropic sources. Siberian Mathematical Journal, Vol. 36, Issue. 3, p. 472.

Kireîtov, V. R. 1997. The stationary translation-invariant Peierls equation of the theory of radiation transport in the space of termpered distributions and some properties of the Peierls potential. II. Siberian Mathematical Journal, Vol. 38, Issue. 4, p. 699.

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Characterizations of Supports of Balayaged Measures

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