Gabor frames on non-Archimedean fields

Abstract

In this paper, we introduce the concept of periodic Gabor frames on non-Archimedean fields of positive characteristic. We first establish a necessary and sufficient condition for a periodic Gabor system to be a Gabor frame for [Formula: see text]. Then, we present some equivalent characterizations of Parseval Gabor frames on non-Archimedean fields by means of some fundamental equations in the time domain. Finally, potential applications of Gabor frames on non-Archimedean fields are also discussed.