Asymptotics of approximation of conjugate functions by Poisson integrals

DOI10.12697/ACUTM.2018.22.19zbMath1440.42001WikidataQ128641081 ScholiaQ128641081MaRDI QIDQ5224262

Yu. I. Kharkevych, Kateryna Pozharska

Publication date: 23 July 2019

Published in: Acta et Commentationes Universitatis Tartuensis de Mathematica (Search for Journal in Brave)

zbMATH Keywords

Poisson integralconjugate functionasymptotic decompositionKolmogorov-Nikol'skii problem

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Trigonometric polynomials, inequalities, extremal problems (42A05)

Related Items (8)

Approximative properties of the three-harmonic Poisson integrals on the classes \({W}_{\beta}^r{H}^{\alpha } \) ⋮ Fourier transform of the summatory Abel-Poisson function ⋮ 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 ⋮ Representation of Weierstrass integral via Poisson integrals ⋮ On the approximation of functions from the Hölder class given on a segment by their biharmonic Poisson operators ⋮ Approximation of the classes $W^{r}_{\beta,\infty}$ by three-harmonic Poisson integrals ⋮ On some asymptotic properties of solutions to biharmonic equations

Cites Work

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• Some properties of operators of Abel-Poisson type
• Approximation properties of Poisson integrals for the classes \(C_\beta^\psi H^\alpha\)
• The complete asymptotic expansion for the measure of approximation of Abel-Poisson's singular integral for Lip 1
• Approximation of (ψ, β)-differentiable functions by Poisson integrals in the uniform metric
• Approximation of functions from the class $ C_{\beta, \infty }^\psi $ by Poisson integrals in the uniform metric
• Approximation of (ψ, β)-Differentiable Functions Defined on the Real Axis by Abel-Poisson Operators
• Sur l'ordre de l'approximation d'une fonction par son intégrale de Poisson

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