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arXiv · 2510.23575

Bessel duality of Gabor systems: A von Neumann algebraic perspective

Ulrik Enstad·Franz Luef
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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.

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Ulrik Enstad, Franz Luef. 2025-10-27. Bessel duality of Gabor systems: A von Neumann algebraic perspective. https://arxiv.org/abs/2510.23575

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