Spherical functions and conformal densities on spherically symmetric <IMG ALIGN=MIDDLE HEIGHT=32 WIDTH=83>-spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Spherical functions and conformal densities on spherically symmetric -spaces

Authors:	Michel Coornaert Athanase Papadopoulos

Institution:	Institut de Recherche Mathématique Avancée, Université Louis Pasteur et CNRS, 7, rue René Descartes, 67084 Strasbourg Cedex France ; Institut de Recherche Mathématique Avancée, Université Louis Pasteur et CNRS, 7, rue René Descartes, 67084 Strasbourg Cedex France

Abstract:	Let be a -space which is spherically symmetric around some point $x_{0}\in X$ and whose boundary has finite positive dimensional Hausdorff measure. Let $\mu =(\mu _{x})_{x\in X}$ be a conformal density of dimension on $\partial X$ . We prove that $\mu _{x_{0}}$ is a weak limit of measures supported on spheres centered at $x_{0}$ . These measures are expressed in terms of the total mass function of $\mu$ and of the dimensional spherical function on . In particular, this result proves that $\mu$ is entirely determined by its dimension and its total mass function. The results of this paper apply in particular for symmetric spaces of rank one and semi-homogeneous trees.

Keywords:

	点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文