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Reproducing properties of hyperbolically-harmonic and -monogenic functions

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Abstract

We shall study the solutions of the Laplace-Beltrami equation associated to certain models of hyperbolic spaces. This problem, first studied byLEUTWILER for the upper half plane case, has been generalized byCNOPS to other models. In this context, there arises the concept ofharmonic andmonogenic functions with respect to the metric of the manifold. The use of the conformal invariance provides an aditional tool for this study.

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In honour of the occasion of Professor Loo-Keng Hua's 90th birthday

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Cerejeiras, P. Reproducing properties of hyperbolically-harmonic and -monogenic functions. AACA 11, 61–66 (2001). https://doi.org/10.1007/BF03219122

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Keywords

  • Laplace-Beltrami equation
  • hyperbolic spaces
  • Poisson-Szegö kernels

MSC 2000

  • 30G35