The Plancherel decomposition for a reductive symmetric space I. Spherical functions

Details The Plancherel decomposition for a reductive symmetric space I. Spherical functions The Plancherel decomposition for a reductive symmetric space I. Spherical functions

2001-07-09

arxiv.org/abs/math/0107063v4

Inventiones Mathematicae 161 (3) 2005, 453 - 566

Mathematics

Representation Theory

110 pages, LaTeX 2e, reference added. Accepted by Invent. Math

Scientific paper

10.1007/s00222-004-0431-y

We prove the Plancherel formula for spherical Schwartz functions on a reductive symmetric space. Our starting point is an inversion formula for spherical smooth compactly supported functions. The latter formula was earlier obtained from the most continuous part of the Plancherel formula by means of a residue calculus. In the course of the present paper we also obtain new proofs of the uniform tempered estimates for normalized Eisenstein integrals and of the Maass-Selberg relations satisfied by the associated C-functions.

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