A quantitative version of the idempotent theorem in harmonic analysis
By Ben Joseph Green, Tom Sanders. 2006
50 citations recorded by the source corpus.
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 // G M(G) is said to be idempotent if /x*/i = //, or alternatively if j5 takes only the values 0 and 1. The Cohen-Helson-Rudin idempotent theorem states that a measure \x is idempotent if and only if the set {7 G G : i2(7) = 1} belongs to the coset ring of G, that is to say we may write L i=i
Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/0e5c81921ed3d846abf513d66941091542743b97
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In Applied Mathematics
In Discrete Mathematics and Combinatorics
- Ehud Hrushovski
- Terence Tao
- Ben Joseph Green
- Emmanuel Breuillard
- Ernie Croot
- Olof Sisask
- E. Szab'o
- László Pyber
Citations in the corpus
- Stable group theory and approximate subgroups (2009, background): “1 suggest a part of a non-commutative Bourgain system as defined in [15], and conjectured by Ben Green in [46] to exist for approximate subgroups.”
- The structure theory of set addition revisited (2012, unknown): “ished for convex coset progressions. The pioneering work here is that of Bourgain [Bou99] which was framed in a level of generality which includes convex coset progressions by Green and the author in [GS08]. (iii) Finally, the result is a rough equivalence: any set satisfying the conclusion of the t”