Wavelet frames on Vilenkin groups and their approximation properties

DOI10.1142/S0219691315500368zbMath1330.42022arXiv1412.2699OpenAlexW2963256169MaRDI QIDQ3451222

Yuri A. Farkov, Elena A. Lebedeva, Maria A. Skopina

Publication date: 10 November 2015

Published in: International Journal of Wavelets, Multiresolution and Information Processing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.2699

zbMATH Keywords

refinable functionapproximation orderscaling functionWalsh functionwavelet frameVilenkin group

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Harmonic analysis on specific compact groups (43A75) Locally compact abelian groups (LCA groups) (22B99)

Related Items (17)

Finite Parseval frames in Walsh analysis ⋮ Wavelet frames related to Walsh functions ⋮ \((H_p-L_p)\)-type inequalities for subsequences of Nörlund means of Walsh-Fourier series ⋮ Tight wavelet frames on zero-dimensional groups. Construction and approximation ⋮ Approximation properties of systems of periodic wavelets on the Cantor group ⋮ On \(p\)-adic tight wavelet frames ⋮ Harmonic analysis on the space of \(M\)-positive vectors ⋮ Construction of periodic wavelet frames generated by the Walsh polynomials ⋮ Step wavelets on Vilenkin groups ⋮ Fourier transform of Dini-Lipschitz functions on locally compact Vilenkin groups ⋮ An analogue of the Titchmarsh theorem for the Fourier transform on locally compact Vilenkin groups ⋮ Some problems in the theory of approximation of functions on locally compact Vilenkin groups ⋮ Parseval frames and the discrete Walsh transform ⋮ Discrete wavelet transforms in Walsh analysis ⋮ Minimum-energy wavelet frames generated by the Walsh polynomials ⋮ Nonhomogeneous dual wavelet frames with the \(p\)-refinable structure in \(L^2(\mathbb{R}^+)\) ⋮ Construction of Parseval Framelets Associated with GMRA on Local Fields of Positive Characteristic

Cites Work

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• Uncertainty principle for the Cantor dyadic group
• Step refinable functions and orthogonal MRA on Vilenkin groups
• On construction of multivariate wavelet frames
• Estimates of the smoothness of dyadic orthogonal wavelets of Daubechies type
• Fractal multiwavelets related to the Cantor dyadic group
• Algorithms for wavelet construction on Vilenkin groups
• Examples of frames on the Cantor dyadic group
• TIGHT WAVELET FRAMES GENERATED BY THE WALSH POLYNOMIALS
• Stability and Orthonormality of Multivariate Refinable Functions
• Compactly supported tight affine spline frames in 𝐿₂(ℝ^{𝕕})
• Orthogonal Wavelets on the Cantor Dyadic Group
• Explicit construction of framelets

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