Functional Analysis and Its Applications

, Volume 42, Issue 4, pp 290–297

Horospherical transform on Riemannian symmetric manifolds of noncompact type

Article

DOI: 10.1007/s10688-008-0042-2

Cite this article as:
Gindikin, S. Funct Anal Its Appl (2008) 42: 290. doi:10.1007/s10688-008-0042-2

Abstract

We discuss I. M. Gelfand’s project of rebuilding the representation theory of semisimple Lie groups on the basis of integral geometry. The basic examples are related to harmonic analysis and the horospherical transform on symmetric manifolds. Specifically, we consider the inversion of this transform on Riemannian symmetric manifolds of noncompact type. In the known explicit inversion formulas, the nonlocal part essentially depends on the type of the root system. We suggest a universal modification of this operator.

Key words

symmetric manifold horospherical transform inversion formula Plancherel formula 

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Departm. of Math., Hill CenterRutgers UniversityPiscatawayUSA

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