Approximating properties of biharmonic Poisson integrals in the classes \(W_\beta^r H^\alpha\)

DOI10.1007/S11253-017-1323-9zbMath1490.42004OpenAlexW2611114974MaRDI QIDQ1729385

Inna V. Kal'chuk, Yu. I. Kharkevych

Publication date: 27 February 2019

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

Full work available at URL: https://doi.org/10.1007/s11253-017-1323-9

zbMATH Keywords

approximations of functionsleast upper boundsasymptotic equalitiesbiharmonic Poisson integrals

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Rate of convergence, degree of approximation (41A25)

Related Items (11)

Approximative properties of the Weierstrass integrals on the classes \( {W}_{\beta}^r{H}^{\alpha } \) ⋮ 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 ⋮ On boundary values of three-harmonic Poisson integral on the boundary of a unit disk ⋮ Asymptotic properties of the solutions of higher-order differential equations on generalized Hölder classes ⋮ Some asymptotic properties of the solutions of Laplace equations in a unit disk ⋮ Approximation of the classes \({W}_{\beta}^r{H}^{\alpha }\) by three-harmonic Poisson integrals ⋮ Approximation of the classes \(C_{\beta}^{\psi } H^\alpha\) by biharmonic Poisson integrals ⋮ Approximation of functions from the classes \(W_\beta^r H^\alpha\) by Weierstrass integrals ⋮ Approximating properties of biharmonic Poisson operators in the classes \(\widehat{L}_{\beta,1}^\psi\) ⋮ Approximative properties of biharmonic Poisson integrals on Hölder classes

Cites Work

• Approximation of functions from the classes \(C_{\beta, \infty}^{\psi}\) by biharmonic Poisson integrals
• Approximation of \((\psi, \beta)\)-differentiable functions of low smoothness by biharmonic Poisson integrals
• Approximation properties of Poisson integrals for the classes \(C_\beta^\psi H^\alpha\)
• Precise inequalities for the oscillations of harmonic and biharmonic functions in a circle
• Approximation of conjugate differentiable functions by biharmonic Poisson integrals
• Asymptotics of the values of approximations in the mean for classes of differentiable functions by using biharmonic Poisson integrals
• Über das Randverhalten des POISSON‐Integrals der polyharmonischen Gleichung
• Tangential limit values of a biharmonic poisson integral in a disk
• On a biharmonic function in the unit disc
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