Approximation of classes \({C}_{\beta, \infty}^{\psi }\) by three-harmonic Poisson integrals in uniform metric (low smoothness)

DOI10.1007/s10958-022-06190-3OpenAlexW4309442705MaRDI QIDQ2683642

Ulyana Z. Hrabova, Inna V. Kal'chuk

Publication date: 14 February 2023

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-022-06190-3

zbMATH Keywords

uniform metricthree-harmonic Poisson integral\(( \psi, \beta )\)-derivative

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Approximation by operators (in particular, by integral operators) (41A35) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)

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Approximation of continuous functions given on the real axis by three-harmonic Poisson operators ⋮ Some applied aspects of the Dirac delta function

Cites Work

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• Multipliers of Fourier series
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• Approximation of the classes \(C_{\beta}^{\psi } H^\alpha\) by biharmonic Poisson integrals
• Stieltjes integrals in the theory of harmonic functions
• Approximation properties of Poisson integrals for the classes \(C_\beta^\psi H^\alpha\)
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• Approximation of (ψ, β)-differentiable functions by Poisson integrals in the uniform metric
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• On approximation of functions from the class $L^{\psi}_{\beta, 1}$ by the Abel-Poisson integrals in the integral metric
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• Some Tauberian theorems with applications to approximation theory

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