Hilbert and Fr\'echet bundle versions of the Harish-Chandra and Whittaker Plancherel Theorems
Representation Theory
2024-10-31 v1
Abstract
This paper, in particular, gives a complete proof of the direct integral version of the Whittaker Plancherel Theorem. The main emphasis is on certain Hilbert and Fr\'echet vector bundles over a space that has a submersion onto the tempered dual. This allows for an approach to the Plancherel Theorems (both for L^2 and the Whittaker case) that is representation theoretic, bypasses the need for Harish-Chandra's Eisenstein Integrals and yields a proof the direct integral decompositions without invoking the abstract theory.
Keywords
Cite
@article{arxiv.2410.23226,
title = {Hilbert and Fr\'echet bundle versions of the Harish-Chandra and Whittaker Plancherel Theorems},
author = {Nolan R. Wallach},
journal= {arXiv preprint arXiv:2410.23226},
year = {2024}
}