The Balian-Low theorem and noncommutative tori
Franz Luef
TL;DR
This paper explores the connection between the Balian-Low theorem, which concerns the limitations of well-localized Gabor bases, and geometric structures called constant curvature connections on modules over noncommutative tori.
Contribution
It establishes a novel link between time-frequency analysis and noncommutative geometry, revealing new insights into the structure of Gabor bases.
Findings
Linked Balian-Low theorem to noncommutative geometry
Identified geometric interpretation of Gabor-Riesz bases limitations
Provided a new perspective on localization constraints in harmonic analysis
Abstract
We point out a link between the theorem of Balian and Low on the non-existence of well-localized Gabor-Riesz bases and a constant curvature connection on projective modules over noncommutative tori.
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