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)).
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| Format: | Journal article |
| Veröffentlicht: |
Springer Verlag
2020
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| Zusammenfassung: | 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)). |
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