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

Abstract

The main aim of this paper is to develop the theory of frame multiresolution analysis (FMRA) in frequency domain on local field of positive characteristic. We first introduce the notion of shift-invariant subspace and the various characteristics of closed shift-invariant subspaces by their fibres in the frequency domain. We define the frame multiresolution analysis in discrete settings on local fields of positive characteristic (LPFC). Furthermore, we established the properties of multiresolution subspaces, which will provide the quantitative criteria for the construction of FMRAs. We also show that the scaling property of an FMRA also holds for the wavelet subspaces and that the Hilbert space L 2 (K) can be decomposed into the orthogonal sum of these wavelet subspaces.