relation: http://acta.bibl.u-szeged.hu/75853/
title: Characterization of Schauder basis property of Gabor systems in local fields
creator:  Behera Biswaranjan
creator:  Molla Md. Nurul
subject: 01. Természettudományok
subject: 01.01. Matematika
description: 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).
date: 2021
type: Cikk, tanulmány, mű
type: NonPeerReviewed
format: part
language: hu
identifier: http://acta.bibl.u-szeged.hu/75853/1/math_087_numb_003-004_517-539.pdf
identifier:    Behera Biswaranjan;  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)   
language: eng