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Holomorphicity of a class of semigroups of measures operating on $ L\sp{p}(G/H)$

Author: Tomasz Przebinda
Journal: Proc. Amer. Math. Soc. 87 (1983), 637-643
MSC: Primary 47D05; Secondary 22E30, 43A10
MathSciNet review: 687632
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Abstract: In the present paper we consider the class of stable semigroups of measures on a Lie group $ G$. This class contains the Gaussian semigroups. We prove that under certain strongly continuous representations of $ G$ acting in $ {L^p}(G/H)$, $ 1 \leqslant p < \infty $, these semigroups are holomorphic and uniformly bounded.

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  • [1] Michel Duflo, Représentations de semi-groupes de mesures sur un groupe localement compact, Ann. Inst. Fourier (Grenoble) 28 (1978), no. 3, xii, 225–249 (French, with English summary). MR 511825
  • [2] A. Hulanicki, A class of convolution semigroups of measures on a Lie group, Probability theory on vector spaces, II (Proc. Second Internat. Conf., Błażejewko, 1979) Lecture Notes in Math., vol. 828, Springer, Berlin, 1980, pp. 82–101. MR 611711
  • [3] -, private communication.
  • [4] G. A. Hunt, Semi-groups of measures on Lie groups, Trans. Amer. Math. Soc. 81 (1956), 264–293. MR 0079232, 10.1090/S0002-9947-1956-0079232-9
  • [5] J. Kisynski, Holomorphicity of semi-groups of operators generated by sublaplacians on Lie groups, Lecture Notes in Math., Springer-Verlag, Berlin and New York.
  • [6] T. Przebinda, Spectrum of convolution operators on $ {L^p}(G/H)$, preprint.
  • [7] V. S. Varadarajan, Lie groups, Lie algebras, and their representations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1974. Prentice-Hall Series in Modern Analysis. MR 0376938
  • [8] K. Yosida, Functional analysis, Springer-Verlag, Berlin, Göttingen and Heidelberg, 1965.

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Keywords: Semigroups of measures, holomorphic semigroups, Lie groups, Haar measure, absolutely continuous measures, group representations
Article copyright: © Copyright 1983 American Mathematical Society