Th\'eor\`eme de Paley-Wiener pour les fonctions de Whittaker sur un groupe r\'eductif p-adique

TL;DR

This paper establishes a Paley-Wiener theorem for the Fourier transform of compactly supported Whittaker functions on reductive p-adic groups, providing a characterization of the transform's image.

Contribution

It introduces a Paley-Wiener theorem specifically for Whittaker functions on reductive p-adic groups, extending harmonic analysis tools in this context.

Findings

Fourier transform of compactly supported Whittaker functions is characterized.

The image of the Fourier transform is explicitly described.

The results generalize classical Paley-Wiener theorems to p-adic groups.

Abstract

We define the Fourier transform of compactly supported Whittaker functions on a reductive p-adic group and we characterize the image of this transformation.