%0 Journal Article
%@ 2064-8316
%A  Behera Biswaranjan
%A  Molla Md. Nurul
%C Szeged
%D 2021
%F acta:75853
%J Acta scientiarum mathematicarum
%K Analízis - matematikai
%N 3-4
%P 517-539
%T Characterization of Schauder basis property of Gabor systems in local fields
%U http://acta.bibl.u-szeged.hu/75853/
%V 87
%X 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).
%Z Bibliogr.: p. 538-539. ; összefoglalás angol nyelven