On the Whittaker Plancherel Theorem for Real Reductive Groups

Abstract

The purpose of this article is to give the first complete proof of the Whittaker Plancherel Theorem. The proof uses Harish-Chandra's Plancherel Theorem for a real reductive group and its exposition can be used as an introduction to Harish-Chandra's ideas. The proof follows the basic ideas in the author's original attempt in his second volume on real reductive groups. An error in the calculation of the Whittaker Transform of a Harish-Chandra wave packet is fixed using a result of Rapha\"el Beuzart-Plessis.