dc.contributor
Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor
Universitat Politècnica de Catalunya. EDP - Grup d'Equacions en Derivades Parcials
dc.contributor.author
Enstad, Ulrik
dc.contributor.author
Thiel, Hannes
dc.contributor.author
Vilalta Vila, Eduard
dc.date.issued
2025-02-28
dc.identifier
Enstad, U.; Thiel, H.; Vilalta, E. Criteria for the existence of schwartz Gabor frames over rational lattices. «International mathematics research notices», 28 Febrer 2025, vol. 2025, núm. 5, article rnaf038, p. 1-12.
dc.identifier
https://hdl.handle.net/2117/449287
dc.identifier
10.1093/imrn/rnaf038
dc.description.abstract
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.
dc.description.abstract
U.E. was supported by The Research Council of Norway through project 314048. H.T. and E.V. were partially supported by the Knut and Alice Wallenberg Foundation (KAW 2021.0140). E.V. was also partially supported by Spanish Research State Agency (grant no. PID2020- 113047GBI00/AEI/10.13039/501100011033) and by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya (grant no. 2021-SGR-01015).
dc.description.abstract
Postprint (published version)
dc.format
application/pdf
dc.relation
https://academic.oup.com/imrn/article/2025/5/rnaf038/8045633
dc.relation
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113047GB-I00/ES/ANILLOS, MODULOS, C*-ALGEBRAS, Y DINAMICA: CLASIFICACION, ESTRUCTURA FINA Y REGULARIDAD/
dc.rights
http://creativecommons.org/licenses/by/4.0/
dc.rights
Attribution 4.0 International
dc.subject
Àrees temàtiques de la UPC::Matemàtiques i estadística
dc.title
Criteria for the existence of schwartz Gabor frames over rational lattices
