We apply the Feynman-Kac formula to compute the λ-Poisson kernels and λ-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 λ-Poisson kernels and λ-Green functions of half-spaces in ℍⁿ and for balls in real and complex hyperbolic spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-1-11,
author = {Tomasz Byczkowski and Jacek Ma\l ecki and Tomasz \.Zak},
title = {Feynman-Kac formula, $\lambda$-Poisson kernels and $\lambda$-Green functions of half-spaces and balls in hyperbolic spaces},
journal = {Colloquium Mathematicae},
volume = {120},
year = {2010},
pages = {201-222},
zbl = {1196.60138},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-1-11}
}
Tomasz Byczkowski; Jacek Małecki; Tomasz Żak. Feynman-Kac formula, λ-Poisson kernels and λ-Green functions of half-spaces and balls in hyperbolic spaces. Colloquium Mathematicae, Tome 120 (2010) pp. 201-222. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-1-11/