On the Whittaker Plancherel Theorem for Real Reductive Groups
arXiv:1705.06787
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 Raphaël Beuzart-Plessis.
This is the tenth and final version of this paper. It supersedes all of the earlier versions and gives a complete proof of the theorem. It also fixes a gap in the previous version involving j_{σ,ν}