Poisson kernels of half–spaces in real hyperbolic spaces

  • Tomasz Byczkowski

    Wrocław University of Technology, Wroclaw, Poland
  • Piotr Graczyk

    Université d'Angers, Angers, France
  • Andrzej Stós

    Université Blaise Pascal, Aubière, France


We provide an integral formula for the Poisson kernel of half-spaces for Brownian motion in real hyperbolic space Hn\mathbb{H}^n. This enables us to find asymptotic properties of the kernel. We also show convergence to the Poisson kernel of the whole space Hn\mathbb{H}^n. For n=3n=3, 44 or 66 we compute explicit formulas for the Poisson kernel itself.

Cite this article

Tomasz Byczkowski, Piotr Graczyk, Andrzej Stós, Poisson kernels of half–spaces in real hyperbolic spaces. Rev. Mat. Iberoam. 23 (2007), no. 1, pp. 85–126

DOI 10.4171/RMI/487