An uncertainty inequality for finite abelian groups

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Let G be a finite abelian group of order n. For a complex valued function f on G let f̂ denote the Fourier transform of f. The classical uncertainty inequality asserts that if f ≠ 0 then supp(f) · supp(f̂) ≥ G . Answering a question o f Terence Tao, the following improvement of (1) is shown: Theorem. Let d1 < d2 be two consecutive divisors of n. If d1 ≤ k = supp(f) ≤ d2 then supp(f̂) ≥ n/d1d2 (d1 + d2 - k). © 2004 Elsevier Ltd. All rights reserved.




Meshulam, R. (2006). An uncertainty inequality for finite abelian groups. European Journal of Combinatorics, 27(1), 63–67.

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