The Whittaker Plancherel theorem appeared as Chapter 15 in my two volume book, Real Reductive Groups. It was meant to be an application of Harish-Chandra’s Plancherel Theorem.  As it turns out, there are serious gaps in the proof given in the books. At the same time as I was doing my research on the subject, Harish-Chandra was also working on it. His approach was very different from mine and appears as part of Volume 5 of his collected works; which consists of three pieces of research by Harish-Chandra that were incomplete at his death and organized and edited by Gangolli and Varadarajan. Unfortunately,  it also does not contain a proof of the theorem. There was a complication in the proof of this result that caused substantial difficulties which had to do with the image of the analog of Harish-Chandra’s method of descent. In this lecture I will explain how one can complete the proof using a recent result of Raphael Beuzzart-Plessis. I will also give an application of the result to the Fourier transforms of automorphic functions at cusps.

(This seminar will be given remotely, but there will still be a live audience in the lecture room.)

[pre-talk at 1:20PM]