Representation and approximation of multivariate functions with mixed smoothness by hyperbolic wavelets

DOI10.1016/J.JMAA.2003.11.023zbMath1055.42023OpenAlexW2016088848MaRDI QIDQ1433372

He Ping Wang

Publication date: 15 June 2004

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.2003.11.023

zbMATH Keywords

best approximationhyperbolic waveletsdecomposition of functionsfunctions with mixed smoothness

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Numerical methods for wavelets (65T60)

Related Items (9)

Approximation of anisotropic classes by wavelets ⋮ Anisotropic de-noising in functional deconvolution model with dimension-free convergence rates ⋮ Multivariate intensity estimation via hyperbolic wavelet selection ⋮ Wavelet approximation and Fourier widths of classes of periodic functions of several variables. I ⋮ Widths between the anisotropic spaces and the spaces of functions with mixed smoothness ⋮ Approximative characteristics of functions from the classes \( {S}_{p,\theta}^{\Omega } B(\mathbb R^d)\) with a given majorant of mixed moduli of continuity ⋮ Hyperbolic wavelet thresholding methods and the curse of dimensionality through the maxiset approach ⋮ Approximating characteristics of the Nikol'skii-Besov classes \({S}_{1,\theta}^rB({\mathbb{R}}^d) \) ⋮ Greedy algorithm for functions with low mixed smoothness

Cites Work

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• Spaces of functions of mixed smoothness from the decomposition point of view
• Approximation of the Besov classes of periodic functions of several variables in the space \(L_ q\)
• Hyperbolic wavelet approximation
• Ten Lectures on Wavelets

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