Frames Associated with Shift-invariant Spaces on Local Fields

Abstract

Abstract. In this paper we present a unified approach to the study of shiftinvariant
systems to be frames on local fields of positive characteristic. We establish a necessary condition and three sufficient conditions under which the shift-invariant systems on local fields of positive characteristic become frames in L2(K). As an application of these results, we obtain some known conclusions about the Gabor frames and wavelet frames on local fields.