Generalized Laplacians for generalized Poisson-Cauchy transforms on classical domains

We develop a group-theoretic method of generalizing the Laplace-Beltrami operators on the classical domains. In [18], we defined the generalized Poisson-Cauchy transforms on the classical domains. We show that the generalized Poisson-Cauchy transforms give us eigenfunctions of the generalized Laplac...

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Veröffentlicht in:	Proceedings of the Japan Academy. Series A. Mathematical sciences 2006-12, Vol.82 (9), p.167-172
Hauptverfasser:	Imamura, Eisuke, Okamoto, Kiyosato, Tsukamoto, Michiroh, Yamamori, Atsushi
Format:	Artikel
Sprache:	eng
Schlagworte:	22E46 32A26 32M15 43A85 analysis on homogeneous spaces Lie group representations Lie groups
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creator	Imamura, Eisuke Okamoto, Kiyosato Tsukamoto, Michiroh Yamamori, Atsushi
description	We develop a group-theoretic method of generalizing the Laplace-Beltrami operators on the classical domains. In [18], we defined the generalized Poisson-Cauchy transforms on the classical domains. We show that the generalized Poisson-Cauchy transforms give us eigenfunctions of the generalized Laplacians defined in this paper.
doi_str_mv	10.3792/pjaa.82.167
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subjects	22E46 32A26 32M15 43A85 analysis on homogeneous spaces Lie group representations Lie groups
title	Generalized Laplacians for generalized Poisson-Cauchy transforms on classical domains
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