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

• 成果类型: Article
• 署名作者: van den Ban, EP; Schlichtkrull, H
• 署名单位: Utrecht University; University of Copenhagen; Aarhus University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-004-0431-y
• 发表日期: 2005
• 页码: 453-566
• 关键词: invariant differential-operators; principal series; eisenstein integrals; distribution vectors; schwartz space; FORMULA; REPRESENTATIONS; inversion

摘要

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.