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arXiv · 2410.23226

Hilbert and Fr\'echet bundle versions of the Harish-Chandra and Whittaker Plancherel Theorems

Nolan R. Wallach
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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.

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BibTeXRIS

Nolan R. Wallach. 2024-10-30. Hilbert and Fr\'echet bundle versions of the Harish-Chandra and Whittaker Plancherel Theorems. https://arxiv.org/abs/2410.23226

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