Tampere University of Technology

TUTCRIS Research Portal

Fundamental solution of k-hyperbolic harmonic functions in odd spaces

Research output: Contribution to journalArticleScientificpeer-review


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


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.

ASJC Scopus subject areas

Publication forum classification

Field of science, Statistics Finland