Hyperbolic function theory in the plane

Presenter: Vesa Vuojamo, Tampere University of Technology, Finland

Joint work with Sirkka-Liisa Eriksson, Heikki Orelma

We study generalized analytic functions and hyperbolic harmonic functions in the upper half plane and generalize the results to higher dimensions. Hyperbolic harmonic functions are solutions of the equation $$\Delta u-\frac{\alpha}{y}\partial_yu=0$$ where $\alpha$ is a real parameter. We consider solutions which depend only on the hyperbolic distance and represent these using Legendre functions.