Information geometry of Poisson kernels on Damek-Ricci spaces
type: Item
instance of: scholarly article
title: Information geometry of Poisson kernels on Damek-Ricci spaces
zbMATH Open document ID: 1196.53034
author: Mitsuhiro Itoh
author: Hiroyasu Satoh
published in: Tokyo Journal of Mathematics
publication date: 2010-08-30T00:00:00Z
review text: The authors prove that the Poisson kernel of a Damek-Ricci space can be represented in terms of the Busemann function. This property implies that the embedding of the Damek-Ricci space into the infinite-dimensional space of probability measures of the boundary (equipped with the Fisher information) is homothetic. The results have been announced in [\textit{M. Itoh} and \textit{H. Sato}, in: Proceedings of the 13th international workshop on differential geometry and related fields, Taegu, Korea, November 5--7, 2009. Taegu: Korean Mathematical Society and Grassmann Research Group 27--36 (2009; Zbl 1196.53033)].
reviewed by: Thomas Friedrich
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 43A85
zbMATH DE Number: 5776103
zbMATH Keywords: Fisher information
zbMATH Keywords: Poisson kernel
zbMATH Keywords: Damek-Ricci space
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1279719582
OpenAlex ID: W1977372486
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DOI: 10.3836/TJM/1279719582
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description: scientific article; zbMATH DE number 5776103