Information geometry of Poisson kernels on Damek-Ricci spaces (Q989204)

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)].