Bounds in Cohen’s idempotent theorem
Suppose that G is a finite Abelian group and write W(G) for the set of cosets of subgroups of G. We show that if f:G→Z satisfies the estimate ∥f∥A(G)≤M with respect to the Fourier algebra norm, then there is some z:W(G)→Z such that f=∑W∈W(G)z(W)1W and ∥z∥ℓ1(W(G))=exp(M4+o(1)).
| Huvudupphovsman: | |
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| Materialtyp: | Journal article |
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Springer Verlag
2020
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| _version_ | 1826286886392430592 |
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| author | Sanders, T |
| author_facet | Sanders, T |
| author_sort | Sanders, T |
| collection | OXFORD |
| description | Suppose that G is a finite Abelian group and write W(G) for the set of cosets of subgroups of G. We show that if f:G→Z satisfies the estimate ∥f∥A(G)≤M with respect to the Fourier algebra norm, then there is some z:W(G)→Z such that
f=∑W∈W(G)z(W)1W and ∥z∥ℓ1(W(G))=exp(M4+o(1)). |
| first_indexed | 2024-03-07T01:50:23Z |
| format | Journal article |
| id | oxford-uuid:99e1bf6c-9b38-478d-aefb-2cef4d0d55c9 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T01:50:23Z |
| publishDate | 2020 |
| publisher | Springer Verlag |
| record_format | dspace |
| spelling | oxford-uuid:99e1bf6c-9b38-478d-aefb-2cef4d0d55c92022-03-27T00:17:30ZBounds in Cohen’s idempotent theoremJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:99e1bf6c-9b38-478d-aefb-2cef4d0d55c9Symplectic ElementsSpringer Verlag2020Sanders, TSuppose that G is a finite Abelian group and write W(G) for the set of cosets of subgroups of G. We show that if f:G→Z satisfies the estimate ∥f∥A(G)≤M with respect to the Fourier algebra norm, then there is some z:W(G)→Z such that f=∑W∈W(G)z(W)1W and ∥z∥ℓ1(W(G))=exp(M4+o(1)). |
| spellingShingle | Sanders, T Bounds in Cohen’s idempotent theorem |
| title | Bounds in Cohen’s idempotent theorem |
| title_full | Bounds in Cohen’s idempotent theorem |
| title_fullStr | Bounds in Cohen’s idempotent theorem |
| title_full_unstemmed | Bounds in Cohen’s idempotent theorem |
| title_short | Bounds in Cohen’s idempotent theorem |
| title_sort | bounds in cohen s idempotent theorem |
| work_keys_str_mv | AT sanderst boundsincohensidempotenttheorem |