Best trigonometric approximations for some classes of periodic functions of several variables in the uniform metric

DOI10.1134/S0001434607070279zbMath1219.41006MaRDI QIDQ635566

A. S. Romanyuk

Publication date: 20 August 2011

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

Hölder's inequalitybest trigonometric approximationMinkowski's inequalityclasses \(B_{p\theta }^{r}\) and \(W_{p\alpha }^{r}\) of periodic functions

Mathematics Subject Classification ID

Multidimensional problems (41A63) Approximation by polynomials (41A10) Convergence of Fourier series and of inverse transforms (43A50)

Related Items

Nonlinear trigonometric approximations of multivariate function classes, Best \(n\)-term approximation of diagonal operators and application to function spaces with mixed smoothness, Characteristics of the linear and nonlinear approximations of the Nikol'skii-Besov-type classes of periodic functions of several variables, Approximations of the classes \(\mathbf{MB}_{p,\theta}^{r}\) of periodic functions of several variables by polynomials according to the Haar system, Best trigonometric and bilinear approximations for the classes of \((\psi,\beta)\)-differentiable periodic functions, Nonlinear approximations of classes of periodic functions of many variables, Approximate characteristics of the classes \({B}_{p,\theta}^{\Omega}\) of periodic functions of one variable and many ones, Estimation of some approximating characteristics of the classes of periodic functions of one and many variables, Approximating characteristics of the Nikol'skii-Besov classes \({S}_{1,\theta}^rB({\mathbb{R}}^d) \), Best orthogonal trigonometric approximations of the Nikol'skii-Besov-type classes of periodic functions in the space \(B_{ \infty ,1}\), Approximation of the classes of periodic functions of one and many variables from the Nikol'skii-Besov and Sobolev spaces

Cites Work

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