Poisson kernels of half – spaces in real hyperbolic spaces

  title={Poisson kernels of half – spaces in real hyperbolic spaces},
  author={Tomasz Byczkowski},
We provide an integral formula for the Poisson kernel of half-spaces for Brownian motion in real hyperbolic space Hn. This enables us to find asymptotic properties of the kernel. Our starting point is the formula for its Fourier transform. When n = 3, 4 or 6 we give an explicit formula for the Poisson kernel itself. In the general case we give various asymptotics and show convergence to the Poisson kernel of Hn. 2000 MS Classification: Primary ; Secondary . 

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