Multiresolution Analysis and Wavelets on Vilenkin Groups
TL;DR: In this paper, a review of multiresolution analysis and compactly ported orthogonal wavelets on Vilenkin groups is presented, where the Strang-Fix condition, the partition of unity property, the linear independence, the stability, and the orthonormality of 'integer shifts' of the corresponding refinable functions are considered.
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Abstract: This paper gives a review of multiresolution analysis and compactly sup- ported orthogonal wavelets on Vilenkin groups. The Strang-Fix condition, the partition of unity property, the linear independence, the stability, and the orthonormality of 'integer shifts' of the corresponding refinable functions are considered. Necessary and sufficient conditions are given for refinable functions to generate a multiresolution analysis in the L2-spaces on Vilenkin groups. Several examples are provided to illustrate these results. .
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Citations
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Ultrametric Pseudodifferential Equations and Applications
Andrei Khrennikov,Sergei Vladimirovich Kozyrev,W. A. Zúñiga-Galindo +2 more
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Step Refinable Functions and Orthogonal MRA on Vilenkin Groups
TL;DR: In this article, necessary and sufficient conditions on refinable step functions under which this function generates an orthogonal MRA in the L 2 -spaces on Vilenkin group were given.
44
Characterization of wavelets and MRA wavelets on local fields of positive characteristic
Biswaranjan Behera,Qaiser Jahan +1 more
TL;DR: In this article, a characterization of wavelets on local fields of positive characteristic based on results on affine and quasi-affine frames is provided, and all wavelets associated with a multiresolution analysis on such a local field are also characterized.
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Algorithms for wavelet construction on Vilenkin groups
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31
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TL;DR: This book presents a development of the basic facts about harmonic analysis on local fields and the "n"-dimensional vector spaces over these fields and focuses almost exclusively on the analogy between the local field and Euclidean cases, with respect to the form of statements, the manner of proof, and the variety of applications.
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Walsh Series, An Introduction to Dyadic Harmonic Analysis
Ferenc Schipp,William R. Wade,Péter L. Simon +2 more
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TL;DR: In this paper, the convergence of Walsh-Fourier coefficients dyadic martingales and Hardy spaces convergence in norm approximation and convergence and summability of uniqueness representation by Walsh series the Walsh Fourier transform.
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