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Fundamental solution of k-hyperbolic harmonic functions in odd spaces

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Details

Original languageEnglish
Article number012034
JournalJournal of Physics: Conference Series
Volume597
Issue number1
DOIs
Publication statusPublished - 13 Apr 2015
Publication typeA1 Journal article-refereed

Abstract

We study k-hyperbolic harmonic functions in the upper half space . The operator is the Laplace-Beltrami operator with respect to the Riemannian metric . In case k = n - 1 the Riemannian metric is the hyperbolic distance of Poincare upper half space. The proposed functions are connected to the axially symmetric potentials studied notably by Weinstein, Huber and Leutwiler. We present the fundamental solution in case n is even using the hyperbolic metric. The main tool is the transformation of k-hyperbolic harmonic functions to eigenfunctions of the hyperbolic Laplace operator.

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Field of science, Statistics Finland