Approximation of functions from the classes \(C_{\beta, \infty}^{\psi}\) by biharmonic Poisson integrals

DOI10.1007/s11253-011-0565-1zbMath1231.41033OpenAlexW1980579338MaRDI QIDQ660685

Yu. I. Kharkevych, K. M. Zhyhallo

Publication date: 4 February 2012

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

Full work available at URL: https://doi.org/10.1007/s11253-011-0565-1

Mathematics Subject Classification ID

Approximate quadratures (41A55) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)

Related Items (12)

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 \((\psi, \beta)\)-differentiable functions of low smoothness by biharmonic Poisson integrals ⋮ Approximative properties of biharmonic Poisson integrals on Hölder classes ⋮ On some asymptotic properties of solutions to biharmonic equations

Cites Work

• 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
• On a biharmonic function in the unit disc
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