Non-Wiener groups with a Gelfand pair
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914346525786112 |
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| author | Carter, Max White, Jared T. |
| author_facet | Carter, Max White, Jared T. |
| contents | Let $G$ be a non-amenable locally compact group and $K$ a compact subgroup of $G$ such that $(G,K)$ is a Gelfand pair. We show that if $G$ admits a suitable boundary representation which is topologically irreducible and not unitarizable, then $G$ is not a Wiener group in the sense that its Fourier transform does not satisfy the analogue of Wiener's Tauberian theorem. As an application, we show that if $G$ is a closed non-compact boundary transitive group of automorphisms of a connected locally finite graph with infinitely many ends, or a split reductive algebraic group over a non-archimedean local field, then $G$ is not Wiener. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20364 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-Wiener groups with a Gelfand pair Carter, Max White, Jared T. Functional Analysis Group Theory Representation Theory Primary: 22D15, Secondary: 22D12, 22D20, 43A20, 43A70, 43A90, 46H10 Let $G$ be a non-amenable locally compact group and $K$ a compact subgroup of $G$ such that $(G,K)$ is a Gelfand pair. We show that if $G$ admits a suitable boundary representation which is topologically irreducible and not unitarizable, then $G$ is not a Wiener group in the sense that its Fourier transform does not satisfy the analogue of Wiener's Tauberian theorem. As an application, we show that if $G$ is a closed non-compact boundary transitive group of automorphisms of a connected locally finite graph with infinitely many ends, or a split reductive algebraic group over a non-archimedean local field, then $G$ is not Wiener. |
| title | Non-Wiener groups with a Gelfand pair |
| topic | Functional Analysis Group Theory Representation Theory Primary: 22D15, Secondary: 22D12, 22D20, 43A20, 43A70, 43A90, 46H10 |
| url | https://arxiv.org/abs/2602.20364 |