Approximative properties of the Weierstrass integrals on the classes \( {W}_{\beta}^r{H}^{\alpha } \)

DOI10.1007/s10958-018-3804-2zbMath1392.41014OpenAlexW2800035414MaRDI QIDQ1645315

Inna V. Kal'chuk, Uliana Z. Grabova, Tetiana A. Stepaniuk

Publication date: 28 June 2018

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

Full work available at URL: https://doi.org/10.1007/s10958-018-3804-2

zbMATH Keywords

Lipschitz conditionKolmogorov-Nikolskii problemWeierstrass integralWeyl-Nagy class

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Approximation by other special function classes (41A30)

Related Items (4)

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 the classes $W^{r}_{\beta,\infty}$ by three-harmonic 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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• Some properties of operators of Abel-Poisson type
• Approximating properties of biharmonic Poisson integrals in the classes \(W_\beta^r H^\alpha\)
• Approximation of functions from the classes \(W_\beta^r H^\alpha\) by Weierstrass integrals
• Approximation properties of Poisson integrals for the classes \(C_\beta^\psi H^\alpha\)
• Approximation of functions from the class $ C_{\beta, \infty }^\psi $ by Poisson integrals in the uniform metric
• Approximation of (ψ, β)-differentiable functions by Weierstrass integrals
• Approximation of (ψ, β)-differentiable functions defined on the real axis by Weierstrass operators
• Approximation of (ψ, β)-Differentiable Functions Defined on the Real Axis by Abel-Poisson Operators
• Approximation of functions defined on the real axis by operators generated by λ-methods of summation of their Fourier integrals

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