Generalized hyperbolic harmonic functions in the plane
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Yksityiskohdat
| Alkuperäiskieli | Englanti |
|---|---|
| Otsikko | Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014 (ICNAAM-2014) |
| Kustantaja | American Institute of Physics Inc. |
| Vuosikerta | 1648 |
| ISBN (painettu) | 9780735412873 |
| DOI - pysyväislinkit | |
| Tila | Julkaistu - 10 maaliskuuta 2015 |
| OKM-julkaisutyyppi | A4 Artikkeli konferenssijulkaisussa |
| Tapahtuma | International Conference of Numerical Analysis and Applied Mathematics - , Kreikka Kesto: 1 tammikuuta 2000 → … |
Conference
| Conference | International Conference of Numerical Analysis and Applied Mathematics |
|---|---|
| Maa | Kreikka |
| Ajanjakso | 1/01/00 → … |
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.