Approximation of \((\psi, \beta)\)-differentiable functions of low smoothness by biharmonic Poisson integrals

DOI10.1007/s11253-012-0616-2zbMath1263.31001OpenAlexW2116569521MaRDI QIDQ1760025

K. M. Zhyhallo, Yu. I. Kharkevych

Publication date: 23 November 2012

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

Full work available at URL: https://doi.org/10.1007/s11253-012-0616-2

zbMATH Keywords

biharmonic operatorKolmogorov-Nikol'skij problem

Mathematics Subject Classification ID

Approximation by operators (in particular, by integral operators) (41A35) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)

Related Items

On the approximation of the classes \(W_\beta^r H^\alpha\) by biharmonic Poisson integrals ⋮ On boundary values of three-harmonic Poisson integral on the boundary of a unit disk ⋮ Approximate characteristics of generalized Poisson operators on Zygmund classes ⋮ Approximation of classes \({C}_{\beta, \infty}^{\psi }\) by three-harmonic Poisson integrals in uniform metric (low smoothness) ⋮ Fourier transform of the summatory Abel-Poisson function ⋮ Some asymptotic properties of the solutions of Laplace equations in a unit disk ⋮ Approximation of the classes \(C_{\beta}^{\psi } H^\alpha\) by biharmonic Poisson integrals ⋮ Approximating properties of biharmonic Poisson integrals in the classes \(W_\beta^r H^\alpha\) ⋮ Approximating properties of biharmonic Poisson operators in the classes \(\widehat{L}_{\beta,1}^\psi\) ⋮ Approximation of the classes $W^{r}_{\beta,\infty}$ by three-harmonic Poisson integrals ⋮ Approximative properties of biharmonic Poisson integrals on Hölder classes ⋮ On some asymptotic properties of solutions to biharmonic equations

Cites Work

• Approximation of functions from the classes \(C_{\beta, \infty}^{\psi}\) by biharmonic Poisson integrals
• Approximation by triangular Fourier sums on classes of continuous periodic functions of two variables
• Approximation of conjugate differentiable functions by biharmonic Poisson integrals
• On the absolute summability of Fourier series of almost-periodic besicovitch functions
• Approximation of (ψ, β)-differentiable functions by Poisson integrals in the uniform metric
• On a biharmonic function in the unit disc
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