Brascamp--Lieb inequalities on locally compact abelian groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912169810984960 |
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| author | Bennett, Jonathan Cowling, Michael G. |
| author_facet | Bennett, Jonathan Cowling, Michael G. |
| contents | We establish a structure theorem for the Brascamp--Lieb constant formulated in the general setting of locally compact abelian groups. This extends and unifies the finiteness characterisations previously known for euclidean spaces and for finitely generated groups and their duals. We place particular emphasis on Fourier invariance throughout, reflecting the fundamental Fourier invariance of Brascamp--Lieb multilinear forms in this context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11514 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Brascamp--Lieb inequalities on locally compact abelian groups Bennett, Jonathan Cowling, Michael G. Functional Analysis 44A12, 22D05 We establish a structure theorem for the Brascamp--Lieb constant formulated in the general setting of locally compact abelian groups. This extends and unifies the finiteness characterisations previously known for euclidean spaces and for finitely generated groups and their duals. We place particular emphasis on Fourier invariance throughout, reflecting the fundamental Fourier invariance of Brascamp--Lieb multilinear forms in this context. |
| title | Brascamp--Lieb inequalities on locally compact abelian groups |
| topic | Functional Analysis 44A12, 22D05 |
| url | https://arxiv.org/abs/2412.11514 |