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...

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Bibliographic Details
Main Authors: Behera Biswaranjan
Molla Md. Nurul
Format: Article
Published: 2021
Series:Acta scientiarum mathematicarum 87 No. 3-4
Kulcsszavak:Analízis - matematikai
Subjects:
doi:10.14232/actasm-021-120-8

Online Access:http://acta.bibl.u-szeged.hu/75853
Description
Summary: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).
Physical Description:517-539
ISSN:2064-8316