Frames associated with shift-invariant spaces on local fields

Abstract

In this paper, we present a unified approach to the study of shift-invariant 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 constitute frames for L 2 (K). As an application of these results, we obtain some known conclusions about the Gabor frames and wavelet frames on local fields.

Nonuniform low-pass filters on non Archimedean local fields

“…They call this a nonuniform multiresolution analysis on local fields of positive characteristic.The notion of nonuniform wavelet frames on non-Archimedean local fields was introduced by Ahmad and Sheikh [12] and established a complete characterization of tight nonuniform wavelet frames on non-Archimedean local fields. More results in this direction can also be found in [1,2,3,4,5,6,7,8,9,10,11,13,41,48,49] and the references therein.…”

Wavelet bi-frames on local fields

“…Jiang et al [18] pointed out a method for constructing orthogonal wavelets on local field K with a constant generating sequence and derived necessary and sufficient conditions for a solution of the refinement equation to generate a multiresolution analysis of L 2 (K). In the series of papers [1,2,3,4,5,6,7,8,30,31,32,33], we have obtained various results related to wavelet and Gabor frames on local fields.…”

Frame multiresolution analysis in discrete settings on local fields of positive characteristic

“…Jiang et al [18] pointed out a method for constructing orthogonal wavelets on local field K with a constant generating sequence and derived necessary and sufficient conditions for a solution of the refinement equation to generate a multiresolution analysis of L 2 (K). In the series of papers [1][2][3][4][5][6][7][8][29][30][31][32], we have obtained various results related to wavelet and Gabor frames on local fields.…”