Uniform temperedness of Whittaker integrals for a real reductive group
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910318094974976 |
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| author | Ban, E. P. van den |
| author_facet | Ban, E. P. van den |
| contents | We study Whittaker vectors (and Jacquet integrals) in the generalized principal series for a real reductive group. A functional equation for them is obtained. This allows to establish uniform estimates for their holomorphic extensions with respect to the continuous induction parameter. Finally, we link the Whittaker vectors to Harish-Chandra's Whittaker integrals for which we then prove uniform tempered estimates. This allows us to establish rapid decay for a class of Fourier transforms on the space of Whittaker Schwartz functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_11044 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniform temperedness of Whittaker integrals for a real reductive group Ban, E. P. van den Representation Theory primary 22E46, secondary 43A30, 43A85 We study Whittaker vectors (and Jacquet integrals) in the generalized principal series for a real reductive group. A functional equation for them is obtained. This allows to establish uniform estimates for their holomorphic extensions with respect to the continuous induction parameter. Finally, we link the Whittaker vectors to Harish-Chandra's Whittaker integrals for which we then prove uniform tempered estimates. This allows us to establish rapid decay for a class of Fourier transforms on the space of Whittaker Schwartz functions. |
| title | Uniform temperedness of Whittaker integrals for a real reductive group |
| topic | Representation Theory primary 22E46, secondary 43A30, 43A85 |
| url | https://arxiv.org/abs/2304.11044 |