The aim of this paper is to give a description of the Poisson kernel and the Green function of balls in the complex hyperbolic space. The description is in terms of the hypergeometric function and unitary spherical harmonics in ℂⁿ.
Autor rozpoczyna swą książkę słowami: This book is intended for those interested in the history of mathematics or statistics and more or less acquainted with the latter. It will also be useful for statisticians. My exposition is based, in the first place, on my own investigations published over some 35 years and monograph (2009) and I stop at the axiomatization of probability and at the birth of the real mathematical statistics, i.e., at Fisher.
We apply the Feynman-Kac formula to compute the λ-Poisson kernels and λ-Green functions for half-spaces or balls in hyperbolic spaces. We present known results in a unified way and also provide new formulas for the λ-Poisson kernels and λ-Green functions of half-spaces in ℍⁿ and for balls in real and complex hyperbolic spaces.
Page 1