Poisson kernels of half–spaces in real hyperbolic spaces

Tomasz Byczkowski, Piotr Graczyk, Andrzej Stós
2007 Revista matemática iberoamericana  
We provide an integral formula for the Poisson kernel of halfspaces for Brownian motion in real hyperbolic space H n . This enables us to find asymptotic properties of the kernel. We also show convergence to the Poisson kernel of the whole space H n . For n = 3, 4 or 6 we compute explicit formulas for the Poisson kernel itself. 2000 Mathematics Subject Classification: Primary: 60J45. Secondary: 58J65.
doi:10.4171/rmi/487 fatcat:6zcy4a7q6jczzkpytvq53zsyji