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A quantitative version of the idempotent theorem in harmonic analysis

Abstract:

Suppose that G is a locally compact abelian group, and write M(G) for the algebra of bounded, regular, complex-valued measures under convolution. A measure \mu in M(G) is said to be idempotent if \mu * \mu = \mu, or alternatively if the Fourier-Stieltjes transform \mu^ takes only the values 0 and 1. The Cohen-Helson-Rudin idempotent theorem states that a measure \mu is idempotent if and only if the set {r in G^ : \mu^(r) = 1} belongs to the coset ring of G^, that is to say we may write \mu^ a...

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
Ann. of Math.
Volume:
168
Issue:
3
Pages:
1025-1054
Publication date:
2006-11-09
DOI:
ISSN:
0003-486X
URN:
uuid:8a506c94-8967-456e-9331-df24df625d79
Source identifiers:
190327
Local pid:
pubs:190327
Keywords:

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