A quantitative Balian-Low theorem

2012/05/01 by Shahaf Nitzan, Nitzan, Shahaf, Jan‐Fredrik Olsen +2
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #Digital Filter Design and Implementation #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Primary 42C15 #Secondary 42A38 #math.CA #math.FA #msc:42A38 #msc:42C15

paper · pdf · doi:10.48550/arxiv.1205.0163

11 pages

arxiv created 2012/05/01 · openalex publication_date 2012/05/01 · arxiv updated 2012/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study functions generating Gabor Riesz bases on the integer lattice. The classical Balian-Low theorem restricts the simultaneous time and frequency localization of such functions. We obtain a quantitative estimate that extends both this result and other related theorems.

Citations

• The wavelet transform, time-frequency localization and signal analysis
• Pseudodifferential operators and Banach algebras in mobile communications

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