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June 2010 Information Geometry of Poisson Kernels on Damek-Ricci Spaces
Mitsuhiro ITOH, Hiroyasu SATOH
Tokyo J. Math. 33(1): 129-144 (June 2010). DOI: 10.3836/tjm/1279719582

Abstract

For Damek-Ricci spaces $(X,g)$ we compute the exact form of the Busemann function which is needed to represent the Poisson kernel of $(X,g)$ in exponential form in terms of the Busemann function and the volume entropy. From this fact, we show that the Poisson kernel map $\varphi: (X,g) \rightarrow (\mathcal{P}(\partial X),G)$ is a homothetic embedding. Here $\mathcal{P}(\partial X)$ is the space of probability measures having positive density function on the ideal boundary $\partial X$ of $X$, and $G$ is the Fisher information metric on $\mathcal{P}(\partial X)$.

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Mitsuhiro ITOH. Hiroyasu SATOH. "Information Geometry of Poisson Kernels on Damek-Ricci Spaces." Tokyo J. Math. 33 (1) 129 - 144, June 2010. https://doi.org/10.3836/tjm/1279719582

Information

Published: June 2010
First available in Project Euclid: 21 July 2010

zbMATH: 1196.53034
MathSciNet: MR2509185
Digital Object Identifier: 10.3836/tjm/1279719582

Rights: Copyright © 2010 Publication Committee for the Tokyo Journal of Mathematics

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Vol.33 • No. 1 • June 2010
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