Feynman–Kac formula, $\lambda$-Poisson kernels and $\lambda$-Green functions of half-spaces and balls in hyperbolic spaces
Volume 118 / 2010
Colloquium Mathematicum 118 (2010), 201-222
MSC: Primary 60J45, 31C12, 60G15; Secondary 60J65.
DOI: 10.4064/cm118-1-11
Abstract
We apply the Feynman–Kac formula to compute the $\lambda$-Poisson kernels and $\lambda$-Green functions for half-spaces or balls in hyperbolic spaces. We present known results in a unified way and also provide new formulas for the $\lambda$-Poisson kernels and $\lambda$-Green functions of half-spaces in ${\mathbb H}^n$ and for balls in real and complex hyperbolic spaces.
