Asymptotics for the Radon transform on hyperbolic spaces
Representation Theory
2013-03-04 v1
Abstract
Let G/H be a hyperbolic space over R C or H, and let K be a maximal compact subgroup of G. Let D denote a certain explicit invariant differential operator, such that the non-cuspidal discrete series belong to the kernel of D. For any L^2-Schwartz function f on G/H, we prove that the Abel transform A(Df) of Df is a Schwartz function. This is an extension of a result established in [2] for K-finite and K\cap H-invariant functions.
Cite
@article{arxiv.1303.0149,
title = {Asymptotics for the Radon transform on hyperbolic spaces},
author = {Nils Byrial Andersen and Mogens Flensted--Jensen},
journal= {arXiv preprint arXiv:1303.0149},
year = {2013}
}