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 L2(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 L2(K).
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Behera, B., Md. Molla, N. Characterization of Schauder basis property of Gabor systems in local fields. ActaSci.Math. 87, 517–539 (2021). https://doi.org/10.14232/actasm-021-120-8
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DOI: https://doi.org/10.14232/actasm-021-120-8