Behera Biswaranjan and Molla Md. Nurul: Characterization of Schauder basis property of Gabor systems in local fields. In: Acta scientiarum mathematicarum, (87) 3-4. pp. 517-539. (2021)
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Abstract
Let K be a totally disconnected, locally compact and nondiscrete field of positive characteristic and D be its ring of integers. We characterize the Schauder basis property of the Gabor systems in K in terms of A2 weights on D × D and the Zak transform Zg of the window function g that generates the Gabor system. We show that the Gabor system generated by g is a Schauder basis for L 2 (K) if and only if |Zg| 2 is an A2 weight on D × D. Some examples are given to illustrate this result. Moreover, we construct a Gabor system which is complete and minimal, but fails to be a Schauder basis for L 2 (K).
| Item Type: | Article |
|---|---|
| Heading title: | Analysis |
| Journal or Publication Title: | Acta scientiarum mathematicarum |
| Date: | 2021 |
| Volume: | 87 |
| Number: | 3-4 |
| ISSN: | 2064-8316 |
| Page Range: | pp. 517-539 |
| Language: | English |
| Publisher: | Bolyai Institute, University of Szeged |
| Place of Publication: | Szeged |
| Related URLs: | http://acta.bibl.u-szeged.hu/75796/ |
| DOI: | 10.14232/actasm-021-120-8 |
| Uncontrolled Keywords: | Analízis - matematikai |
| Additional Information: | Bibliogr.: p. 538-539. ; összefoglalás angol nyelven |
| Subjects: | 01. Natural sciences 01. Natural sciences > 01.01. Mathematics |
| Date Deposited: | 2022. May. 24. 12:46 |
| Last Modified: | 2026. Feb. 18. 11:44 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/75853 |
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