Poisson kernels of half-spaces in real hyperbolic spaces

Details Poisson kernels of half-spaces in real hyperbolic spaces Poisson kernels of half-spaces in real hyperbolic spaces

2005-03-17

arxiv.org/abs/math/0503372v1

Mathematics

Probability

Scientific paper

We provide an integral formula for the Poisson kernel of half-spaces for Brownian motion in real hyperbolic space $\H^n$. 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 $\H^n$.

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