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math.FA2026
The frame set of the first Hermite function
Markus Faulhuber, Philipp Petersen
We determine the frame set of the first Hermite function, thereby proving a conjecture of Lyubarskii and Nes. A characterization of semi-regular Gabor frames due to Gröchenig, Rome…
math.FA2026
Linear dependence of time-frequency shifts of a Schwartz function
Markus Faulhuber, Philipp Petersen, Jordy Timo van Velthoven +1
We show that a finite number of time-frequency shifts of a Schwartz function can be linearly dependent. This disproves the so-called HRT conjecture of Heil, Ramanathan, and Topiwal…