Approximation properties of Poisson integrals for the classes \(C_\beta^\psi H^\alpha\)

DOI10.1134/S0001434614110406zbMath1326.42002MaRDI QIDQ2343950

Yanyan Li

Publication date: 11 May 2015

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

zbMATH Keywords

approximationFourier seriesKolmogorov-Nikol'skii problemPoisson integrals

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Summability and absolute summability of Fourier and trigonometric series (42A24)

Related Items (12)

Approximative properties of the Weierstrass integrals on the classes \( {W}_{\beta}^r{H}^{\alpha } \) ⋮ Finding solution subspaces of the Laplace and heat equations isometric to spaces of real functions, and some of their applications ⋮ Approximative properties of the three-harmonic Poisson integrals on the classes \({W}_{\beta}^r{H}^{\alpha } \) ⋮ On the approximation of the classes \(W_\beta^r H^\alpha\) by biharmonic Poisson integrals ⋮ Asymptotic properties of the solutions of higher-order differential equations on generalized Hölder classes ⋮ Approximation of classes \({C}_{\beta, \infty}^{\psi }\) by three-harmonic Poisson integrals in uniform metric (low smoothness) ⋮ Approximation of the classes \(C_{\beta}^{\psi } H^\alpha\) by biharmonic Poisson integrals ⋮ Approximating properties of biharmonic Poisson integrals in the classes \(W_\beta^r H^\alpha\) ⋮ Complete asymptotics of the approximation of function from the Sobolev classes by the Poisson integrals ⋮ Approximation of the classes $W^{r}_{\beta,\infty}$ by three-harmonic Poisson integrals ⋮ Asymptotics of approximation of conjugate functions by Poisson integrals ⋮ Isometry of the subspaces of solutions of systems of differential equations to the spaces of real functions

Cites Work

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• Approximation of differentiable functions by Rogosinski polynomials
• Approximation of the classes C β ψ H ω by generalized Zygmund sums
• Approximation of (ψ, β)-differentiable functions by Poisson integrals in the uniform metric
• Approximation of functions from the class $ C_{\beta, \infty }^\psi $ by Poisson integrals in the uniform metric

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