Bessel duality of Gabor systems: A von Neumann algebraic perspective
Functional Analysis
2025-10-28 v1 Operator Algebras
Abstract
Bessel duality of regular Gabor systems states that a Gabor system over a lattice is a Bessel sequence if and only if the corresponding Gabor system over the adjoint lattice is a Bessel sequence. We show that this fundamental result of time-frequency analysis can be deduced from a theorem in the theory of bimodules over von Neumann algebras, namely that under certain conditions, their left and right bounded vectors coincide.
Cite
@article{arxiv.2510.23575,
title = {Bessel duality of Gabor systems: A von Neumann algebraic perspective},
author = {Ulrik Enstad and Franz Luef},
journal= {arXiv preprint arXiv:2510.23575},
year = {2025}
}
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12 pages