Generalized Laplacians for generalized Poisson-Cauchy transforms on classical domains

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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Zusammenfassung: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.
ISSN:0386-2194
DOI:10.3792/pjaa.82.167