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Journal of Lie Theory 11 (2001), No. 2, 469--481
Copyright Heldermann Verlag 2001

Brownian Motion and the Heat Kernels of Iwasawa NA-Type Groups

M. J. Cornwall
1 Martin Place, Sydney N.S.W. 2000, Australia

Let G be a semisimple Lie group with a finite centre and Iwasawa decomposition NAK. We shall consider the heat equation on NA and prove a structure theorem for a diffusion on the group which is typically called a Brownian motion. This theorem then shows how we may calculate the heat kernel of real hyperbolic space in a relatively easy fashion.

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