Characterization of Schauder basis property of Gabor systems in local fields
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...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2021
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| Sorozat: | Acta scientiarum mathematicarum
87 No. 3-4 |
| Kulcsszavak: | Analízis - matematikai |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-021-120-8 |
| Online Access: | http://acta.bibl.u-szeged.hu/75853 |
| Tartalmi kivonat: | 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). |
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| Terjedelem/Fizikai jellemzők: | 517-539 |
| ISSN: | 2064-8316 |