Generalized hyperbolic harmonic functions in the plane

Sirkka-Liisa Eriksson, Heikki Orelma, Vesa Vuojamo

    Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review


    We consider solutions of the equation yΔh (x,y)-k ah/ay=0 in the plane. These functions already have been investigated by Weinstein around 1950 in connection of generalized axially symmetric potential theory. We have found several results concerning these type of functions, called k-hyperbolic harmonic functions, in higher dimensions. In this paper, we show in the plane case that it is possible to compute the explicit fundamental solutions in terms of the hyperbolic metric. These results may be used to find fundamental solutions in all even dimensional spaces. The key tools are the transformation properties of hyperbolic metric of the Poincaré upper half space model.

    Original languageEnglish
    Title of host publicationProceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014 (ICNAAM-2014)
    Publication statusPublished - 10 Mar 2015
    Publication typeA4 Article in a conference publication
    EventInternational Conference of Numerical Analysis and Applied Mathematics - , Greece
    Duration: 1 Jan 2000 → …


    ConferenceInternational Conference of Numerical Analysis and Applied Mathematics
    Period1/01/00 → …


    • axially symmetric
    • fundamental solution
    • Hyperbolic
    • Laplace-Beltrami

    Publication forum classification

    • Publication forum level 0

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

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