Approximations of the classes \(\mathbf{MB}_{p,\theta}^{r}\) of periodic functions of several variables by polynomials according to the Haar system

DOI10.1007/S10958-015-2549-4zbMath1342.41009OpenAlexW1464197306MaRDI QIDQ904548

Sergei A. Stasyuk

Publication date: 13 January 2016

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-015-2549-4

zbMATH Keywords

Haar systembest \(m\)-term approximationapproximation of functions of several variablesstep-hyperbolic cross

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Multidimensional problems (41A63) Approximation by polynomials (41A10)

Cites Work

• Best trigonometric approximations for some classes of periodic functions of several variables in the uniform metric
• Best \(m\)-term approximation of the classes \(B_{\infty, \theta}^{r}\) of functions of many variables by polynomials in the Haar system
• Approximation of functions in several variables from classes \(H^{\Omega}_p\) by polynomials with respect to the Haar system
• The best \(m\)-term approximation and greedy algorithms
• Nonlinear methods of approximation
• On best \(m\)-term approximations and the entropy of sets in the space \(L^ 1\)
• DIAMETERS OF SETS IN NORMED LINEAR SPACES AND THE APPROXIMATION OF FUNCTIONS BY TRIGONOMETRIC POLYNOMIALS
• Best $ M$-term trigonometric approximations of Besov classes of periodic functions of several variables
• Approximation of classes of periodic functions of several variables
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