Title

Paley–Wiener theorem for line bundles over compact symmetric spaces and new estimates for the Heckman–Opdam hypergeometric functions

Document Type

Article

Publication Date

10-1-2018

Abstract

Paley–Wiener type theorems describe the image of a given space of functions, often compactly supported functions, under an integral transform, usually a Fourier transform on a group or homogeneous space. In this article we proved a Paley–Wiener theorem for smooth sections f of homogeneous line bundles on a compact Riemannian symmetric space U/K. It characterizes f with small support in terms of holomorphic extendability and exponential growth of their χ-spherical Fourier transforms, where χ is a character of K. An important tool in our proof is a generalization of Opdam's estimate for the hypergeometric functions associated to multiplicity functions that are not necessarily positive. At the same time the radius of the domain where this estimate is valid is increased. This is done in an appendix.

Publication Source (Journal or Book title)

Mathematische Nachrichten

First Page

2204

Last Page

2228

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