Non-Uniform Wavelet Frames on Local Fields

Abstract

Tight wavelet frames are distinct from the orthonormal wavelets because of redundancy. By relinquishing orthonormality and permitting redundancy, the tight wavelet frames turn out to be significantly easier to construct than the orthonormal wavelets. In this paper, we introduce a notion of nonuniform wavelet system on nonarchimedean local fields of positive characteristic and gave a complete characterization of such systems to be tight nonuniform wavelet frames on local fields of positive characteristic by using Fourier transforms.

Key words and phrases. Nonuniform MRA, Wavelet frame, Local field, Fourier transform.

2000 Mathematics Subject Classification. 43A70, 42C40, 11S85, 42C15