Criteria for the Existence of Schwartz Gabor Frames Over Rational Lattices
Artikel i vetenskaplig tidskrift, 2025

We give an explicit criterion for a rational lattice in the time-frequency plane to admit a Gabor frame with window in the Schwartz class. The criterion is an inequality formulated in terms of the lattice covolume, the dimension of the underlying Euclidean space, and the index of an associated subgroup measuring the degree of non-integrality of the lattice. For arbitrary lattices we also give an upper bound on the number of windows in the Schwartz class needed for a multi-window Gabor frame.

Författare

Ulrik Enstad

Universitetet i Oslo

Hannes Thiel

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Eduard Vilalta Vila

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Göteborgs universitet

International Mathematics Research Notices

1073-7928 (ISSN) 1687-0247 (eISSN)

Vol. 2025 5 rnaf038

Ämneskategorier (SSIF 2025)

Matematisk analys

DOI

10.1093/imrn/rnaf038

Mer information

Senast uppdaterat

2025-03-26