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Characterization of Relative Domination Principle

Published online by Cambridge University Press:  22 January 2016

Isao Higuchi  and
Masayuki Itô
Isao Higuchi
Affiliation:
Suzuka College of Technology, Nagoya University
Masayuki Itô
Affiliation:
Suzuka College of Technology, Nagoya University
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Let X be a locally compact and σ-compact Abelian group and ξ be the Haar measure of X. A positive Radon measure N on X is called a convolution kernel when we regard it as a kernel of potentials of convolution type. M. Itô [4], [6] characterized the convolution kernel which satisfies the domination principle. The purpose of this paper is to characterize the relative domination principle for the convolution kernels.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 50 , June 1973 , pp. 175 - 184
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1973

References

[1] Choquet, G. and Deny, J.: Sur l’équation de convolution η = η*σ, C. R. Acad. Sc. Paris, 250, 1960, p. 799–801.Google Scholar
[2] Deny, J.: Familles fondamentales: noyaux associés, Ann. Inst. Fourier, 3, 1951, p. 76–101.CrossRefGoogle Scholar
[3] Deny, J.: Noyaux de convolution de Hunt et noyaux associés à une famille fondamentale, Ann. Inst. Fourier, 12, 1962, p. 643–667.Google Scholar
[4] Itô, M.: Noyaux de convolution réguliers et noyaux de convolution singuliers, Nagoya Math. J., 44, 1971, p. 61–77.CrossRefGoogle Scholar
[5] Itô, M.: Sur le principe de domination pour les noyaux de convolution (to appear).Google Scholar
[6] Itô, M.: Une caractérisation du principe de domination pour les noyaux de convolution (to appear).Google Scholar