Multiresolution analysis on product of zero-dimensional Abelian groups

DOI10.1016/j.jmaa.2011.07.043zbMath1229.42041OpenAlexW2081319998MaRDI QIDQ641675

S. F. Lukomskii

Publication date: 24 October 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.07.043

zbMATH Keywords

multiresolution analysiswavelet\(p\)-adic numberszero-dimensional group

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Analysis on specific locally compact and other abelian groups (43A70)

Related Items

Explicit construction of wavelet frames on locally compact abelian groups, Periodic Wavelet Frames on Local Fields of Positive Characteristic, Frame multiresolution analysis on local fields of positive characteristic, Biorthogonal wavelets on local fields of positive characteristic, Tight wavelet frames on zero-dimensional groups. Construction and approximation, Tight framelet packets on local fields of positive characteristic, Characterization of wavelets and MRA wavelets on local fields of positive characteristic, Explicit formula for MRA-wavelets on local fields, Nonuniform multiresolution analysis on local fields of positive characteristic, Wavelets on compact abelian groups

Cites Work

• The Cauchy problems for evolutionary pseudo-differential equations over \(p\)-adic field and the wavelet theory
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• \(p\)-adic orthogonal wavelet bases
• \(p\)-adic refinable functions and MRA-based wavelets
• Non-Haar \(p\)-adic wavelets and their application to pseudo-differential operators and equations
• \(p\)-adic nonorthogonal wavelet bases
• Fractal multiwavelets related to the Cantor dyadic group
• Quincunx multiresolution analysis for \(L^2(\mathbb Q^2_2)\)
• A wavelet theory for local fields and related groups
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• Biorthogonal dyadic wavelets on $ \mathbb R_+$
• Wavelet theory as $ p$-adic spectral analysis
• Orthogonal Wavelets on the Cantor Dyadic Group
• Multiresolution analysis on zero-dimensional Abelian groups and wavelets bases
• Approximation by dyadic wavelets
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