Poisson kernels of half-spaces in real hyperbolic spaces
Byczkowski, Tomasz ; Graczyk, Piotr ; Stós, Andrzej
Rev. Mat. Iberoamericana, Tome 23 (2007) no. 1, p. 85-126 / Harvested from Project Euclid
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We provide an integral formula for the Poisson kernel of half-spaces for Brownian motion in real hyperbolic space $\mathbb{H}^n$. This enables us to find asymptotic properties of the kernel. We also show convergence to the Poisson kernel of the whole space $\mathbb{H}^n$. For $n=3$, $4$ or $6$ we compute explicit formulas for the Poisson kernel itself.
Publié le : 2007-04-14
Classification:  hyperbolic spaces,  Brownian motion,  Poisson kernel,  60J45,  58J65 
@article{1180728886,
     author = {Byczkowski, Tomasz and Graczyk, Piotr and St\'os, Andrzej},
     title = {Poisson kernels of half-spaces in real hyperbolic spaces},
     journal = {Rev. Mat. Iberoamericana},
     volume = {23},
     number = {1},
     year = {2007},
     pages = { 85-126},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1180728886}
}

Byczkowski, Tomasz; Graczyk, Piotr; Stós, Andrzej. Poisson kernels of half-spaces in real hyperbolic spaces. Rev. Mat. Iberoamericana, Tome 23 (2007) no. 1, pp.  85-126. http://gdmltest.u-ga.fr/item/1180728886/