## Abstract

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 language | English |
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Title of host publication | Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014 (ICNAAM-2014) |

Volume | 1648 |

DOIs | |

Publication status | Published - 10 Mar 2015 |

Publication type | A4 Article in a conference publication |

Event | International Conference of Numerical Analysis and Applied Mathematics - , Greece Duration: 1 Jan 2000 → … |

### Conference

Conference | International Conference of Numerical Analysis and Applied Mathematics |
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Country | Greece |

Period | 1/01/00 → … |

## Keywords

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

## Publication forum classification

- Publication forum level 0

## ASJC Scopus subject areas

- Physics and Astronomy(all)