Spherical functions andconformal densities on spherically symmetric CAT (
نویسندگان
چکیده
| Let X be a CAT ( 1) space which is spherically symmetric around some point x0 2 X and whose boundary has nite positive s dimensional Hausdor measure. Let = ( x)x2X be a conformal density of dimension d > s=2 on @X. We prove that x0 is a weak limit of measures supported on spheres centered at x0. These measures are expressed in terms of the total mass function of and of the d dimensional spherical function on X. In particular, this result proves that 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.
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