Geodesic
Feynman–Kac formula, $\lambda$-Poisson kernels and $\lambda$-Green functions of half-spaces and balls in hyperbolic spaces
Tomasz Byczkowski1 ; Jacek Małecki1 ; Tomasz Żak1
1 Institute of Mathematics and Computer Science Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
Colloquium Mathematicum, Tome 118 (2010) no. 1, pp. 201-222

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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.
DOI : 10.4064/cm118-1-11
Keywords: apply feynman kac formula compute lambda poisson kernels lambda green functions half spaces balls hyperbolic spaces present known results unified provide formulas lambda poisson kernels lambda green functions half spaces mathbb balls real complex hyperbolic spaces

Tomasz Byczkowski 1 ; Jacek Małecki 1 ; Tomasz Żak 1

1 Institute of Mathematics and Computer Science Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland 
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Tomasz Byczkowski; Jacek Małecki; Tomasz Żak. Feynman–Kac formula, $\lambda$-Poisson kernels and
$\lambda$-Green functions of half-spaces and balls
in hyperbolic spaces. Colloquium Mathematicum, Tome 118 (2010) no. 1, pp. 201-222. doi: 10.4064/cm118-1-11

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