An uncertainty inequality for finite abelian groups

2003/12/22 by Roy Meshulam, Meshulam, Roy · 2 citations
Computer Science · Mathematics · #20K01 (secondary) #65T50 (primary) #Combinatorics (math.CO) #Cryptography and Residue Arithmetic #Digital Filter Design and Implementation #FOS: Mathematics #Mathematical Analysis and Transform Methods #math.CO #msc:20K01 #msc:65T50

paper · pdf · doi:10.48550/arxiv.math/0312407

7 pages, no figures

arxiv created 2003/12/22 · openalex publication_date 2003/12/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite abelian group of order n. For a complex valued function f on G, let \fht denote the Fourier transform of f. The uncertainty inequality asserts that if f ≠ 0 then |supp(f)| |supp(\fht)| ≥ n. Answering a question of Terence Tao, the following improvement of the classical inequality is shown: Let d₁

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