A characterization of tight wavelet frames on local fields of positive characteristic

Shah, Firdous A.; Abdullah, Abdullah

doi:10.3103/s1068362314060016

Cited by 18 publications

(17 citation statements)

References 15 publications

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“…Recently, Shah and Abdullah [12] have introduced the notion of nonuniform multiresolution analysis on local field of positive characteristic and obtained the necessary and sufficient condition for a function to generate a nonuniform multiresolution analysis on local fields. More results in this direction can also be found in [13,14] and the references therein.…”

Section: Introductionmentioning

confidence: 81%

Frame Multiresolution Analysis on Local Fields of Positive Characteristic

Shah

2015

Journal of Operators

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We present a notion of frame multiresolution analysis on local fields of positive characteristic based on the theory of shift-invariant spaces. In contrast to the standard setting, the associated subspace V0 of L2(K) has a frame, a collection of translates of the scaling function φ of the form φ(·-u(k)):k∈N0, where N0 is the set of nonnegative integers. We investigate certain properties of multiresolution subspaces which provides the quantitative criteria for the construction of frame multiresolution analysis (FMRA) on local fields of positive characteristic. Finally, we provide a characterization of wavelet frames associated with FMRA on local field K of positive characteristic using the shift-invariant space theory.

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Section: Introductionmentioning

confidence: 81%

Frame Multiresolution Analysis on Local Fields of Positive Characteristic

Shah

2015

Journal of Operators

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“…Later on, they have obtained a necessary condition and a set of sufficient conditions for the wavelet system ψ j,k =: q j/2 ψ p − j x − u(k) : j, k ∈ N 0 to be a tight wavelet frame on local fields in the frequency domain in [16]. The characterizations of tight wavelet frames on local fields were completely established by Shah and Abdullah [24] by virtue of two basic equations in the Fourier domain. These studies were continued by Shah and his colleagues in [1,22,23,[25][26][27], where they have described some algorithms for constructing periodic wavelet frames, wave packet frames and semi-orthogonal wavelet frames on local fields of positive characteristic.…”

Section: Introductionmentioning

confidence: 99%

Frames associated with shift-invariant spaces on local fields

Shah¹,

Ahmad²,

Rahimi³

2018

Filomat

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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.

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“…They provide a sufficient condition for finite number of functions {ψ 1 , ψ 2 , ..., ψ L } to form a tight wavelet frame for L 2 (K). As far as the characterization of wavelet frames on local fields is concerned, Shah and Abdullah [27] have established a complete characterization of tight wavelet frames on local fields by virtue of two basic equations in the frequency domain and proved how to construct an orthonormal wavelet basis for L 2 (K). More results in this direction can also be found in [26,28] and the references therein.…”

Section: Introductionmentioning

confidence: 99%