Harmonic analysis of spherical functions on reductive groups over p-adic fields

Marko Tadić

Vol. 109 (1983), No. 1, 215–235

DOI: 10.2140/pjm.1983.109.215

Abstract

We introduce spaces 𝒞^γ(G,K), 0 < γ ≤ 2, of rapidly decreasing K-bi-invariant functions on a reductive p-adic group G where K is a maximal compact subgroup of G, and we study spherical transformations on these spaces. The image of 𝒞^γ(G,K) under spherical transformation is completely described when K is a standard maximal compact subgroup of G.

Mathematical Subject Classification 2000

Primary: 43A90

Secondary: 22E35, 22E50

Milestones

Received: 10 October 1981

Published: 1 November 1983