Generalized Laplacians for generalized Poisson-Cauchy transforms on classical domains

Eisuke Imamura; Kiyosato Okamoto; Michiroh Tsukamoto; Atsushi Yamamori

doi:10.3792/pjaa.82.167

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December 2006 Generalized Laplacians for generalized Poisson-Cauchy transforms on classical domains

Eisuke Imamura, Kiyosato Okamoto, Michiroh Tsukamoto, Atsushi Yamamori

Proc. Japan Acad. Ser. A Math. Sci. 82(9): 167-172 (December 2006). DOI: 10.3792/pjaa.82.167

Abstract

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.

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Eisuke Imamura. Kiyosato Okamoto. Michiroh Tsukamoto. Atsushi Yamamori. "Generalized Laplacians for generalized Poisson-Cauchy transforms on classical domains." Proc. Japan Acad. Ser. A Math. Sci. 82 (9) 167 - 172, December 2006. https://doi.org/10.3792/pjaa.82.167