Author

P. Petersen

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Preprint Sep 2026

The frame set of the first Hermite function

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 Gr\"ochenig, Romero, and St\"ockler reduces the problem to a uniqueness question for entire functions in a Gaussian shift-invariant space. We address this...

Markus Faulhuber, P. Petersen · 1 citation

Preprint Sep 2026

The frame set of the first Hermite function

We determine the frame set of the first Hermite function, proving a conjecture of Lyubarskii and Nes. We use a characterization of semi-regular Gabor frames due to Gr\"ochenig, Romero, and St\"ockler to transform the problem into a question about the existence of a nonzero Gaussian shift-invariant entire function $F$,...

Markus Faulhuber, P. Petersen · 1 citation