A remark on a trace Paley–Wiener theorem

Goran Muić

Vol. 308 (2020), No. 2, 407–418

DOI: 10.2140/pjm.2020.308.407

Abstract

We prove a version of a trace Paley–Wiener theorem for tempered representations of a reductive $p$-adic group. This is applied to complete certain investigations of Shahidi on the proof that a Plancherel measure is an invariant of an $L$-packet of discrete series.

Keywords

Paley–Wiener theorem, admissible representations, reductive $p$-adic groups

Mathematical Subject Classification

Primary: 22E50

Secondary: 11E70

Milestones

Received: 5 January 2019

Revised: 10 January 2020

Accepted: 23 May 2020

Published: 9 December 2020