Hilbert and Fréchet bundle versions of the Harish-Chandra and Whittaker Plancherel Theorems
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909372659007488 |
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| author | Wallach, Nolan R. |
| author_facet | Wallach, Nolan R. |
| contents | 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 Fréchet 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23226 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hilbert and Fréchet bundle versions of the Harish-Chandra and Whittaker Plancherel Theorems Wallach, Nolan R. Representation Theory 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 Fréchet 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. |
| title | Hilbert and Fréchet bundle versions of the Harish-Chandra and Whittaker Plancherel Theorems |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2410.23226 |