Cuspidal hypergeometric functions

1998/08/06 by Eric M. Opdam, Eric Opdam, Opdam, Eric M.
Mathematics · Physics and Astronomy · #33C80 #35P10 #Advanced Algebra and Geometry #FOS: Mathematics #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Representation Theory (math.RT) #Spectral Theory (math.SP) #math.RT #math.SP #msc:33C80 #msc:35P10

paper · pdf · doi:10.48550/arxiv.math/9808035

18 pages, no figures. This paper is dedicated to Richard Askey, on the occasion of his 65th birthday. It will appear in a special issue of Methods and Applications of Analysis

arxiv created 1998/08/06 · openalex publication_date 1998/08/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the Plancherel formula for hypergeometric functions associated to a root system in the situation when the root multiplicities are negative (but close to 0). As a result we obtain a classification of the hypergeometric functions that are square integrable, and we find a closed formula for their square norm as a function of the root multiplicities.

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