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]