Abstract
We show that if the Gabor system { g(x- t) e2πisx} , t∈ T, s∈ S, is an orthonormal basis in L2(R) and if the window function g is compactly supported, then both the time shift set T and the frequency shift set S must be periodic. To prove this we establish a necessary functional tiling type condition for Gabor orthonormal bases which may be of independent interest.
| Original language | English |
|---|---|
| Pages (from-to) | 1461-1467 |
| Number of pages | 7 |
| Journal | Mathematische Annalen |
| Volume | 384 |
| Issue number | 3-4 |
| DOIs | |
| State | Published - Dec 2022 |
Bibliographical note
Publisher Copyright:© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Funding
Research supported by ISF Grants Nos. 447/16, 227/17 and 1044/21 and ERC Starting Grant No. 713927. Alberto Debernardi Pinos was also partially supported by Ministry of Education and Science of the Republic of Kazakhstan (AP08053326), and by The Center for Research & Development in Mathematics and Applications, through the Portuguese Foundation for Science and Technology (UIDP/04106/2020).
| Funders | Funder number |
|---|---|
| Horizon 2020 Framework Programme | 713927 |
| European Commission | |
| Fundação para a Ciência e a Tecnologia | UIDP/04106/2020 |
| Israel Science Foundation | 1044/21, 227/17, 447/16 |
| Ministry of Education and Science of the Republic of Kazakhstan | AP08053326 |
| Center for Research and Development in Mathematics and Applications |