On Characterization of Nonuniform Tight Wavelet Frames on Local Fields

Sheikh, Owais Ahmad Neyaz A.

doi:10.4208/ata.2018.v34.n2.4

Cited by 14 publications

(1 citation statement)

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Ahmad¹,

Sheikh²,

Ahmadini³

et al. 2021

Eur. J. Math. Appl.

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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.

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