Generalized Laplacians for generalized Poisson-Cauchy transforms on classical domains
Eisuke Imamura, K. Okamoto, Michiroh Tsukamoto, Atsushi Yamamori · Proceedings of the Japan Academy Series A Mathematical Sciences · 2006
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.