Feynman–Kac formula, $\lambda$-Poisson kernels and $\lambda$-Green functions of half-spaces and balls in hyperbolic spaces

Volume 118 / 2010

Tomasz Byczkowski, Jacek Małecki, Tomasz Żak 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.

Authors

  • Tomasz ByczkowskiInstitute of Mathematics and Computer Science
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail
  • Jacek MałeckiInstitute of Mathematics and Computer Science
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail
  • Tomasz ŻakInstitute of Mathematics and Computer Science
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail

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