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TUTCRIS

Generalized hyperbolic harmonic functions in the plane

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Yksityiskohdat

AlkuperäiskieliEnglanti
OtsikkoProceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014 (ICNAAM-2014)
KustantajaAmerican Institute of Physics Inc.
Vuosikerta1648
ISBN (painettu)9780735412873
DOI - pysyväislinkit
TilaJulkaistu - 10 maaliskuuta 2015
OKM-julkaisutyyppiA4 Artikkeli konferenssijulkaisussa
TapahtumaInternational Conference of Numerical Analysis and Applied Mathematics - , Kreikka
Kesto: 1 tammikuuta 2000 → …

Conference

ConferenceInternational Conference of Numerical Analysis and Applied Mathematics
MaaKreikka
Ajanjakso1/01/00 → …

Tiivistelmä

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.

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