Approximations on classes of Poisson integrals by Fourier-Chebyshev rational integral operators

DOI10.1134/S0037446621020099zbMath1460.42003OpenAlexW3144814886WikidataQ114075223 ScholiaQ114075223MaRDI QIDQ2661745

P. G. Potseiko, E. A. Rovba

Publication date: 8 April 2021

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

Full work available at URL: https://doi.org/10.1134/s0037446621020099

zbMATH Keywords

Fourier seriesasymptotic estimatespointwise and uniform approximationaccurate constantsclass of Poisson integralsrational integral operators

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Best approximation, Chebyshev systems (41A50) Approximation by operators (in particular, by integral operators) (41A35)

Related Items (5)

On estimates of uniform approximations by rational Fourier-Chebyshev integral operators for a certain choice of poles ⋮ The De La Vallée Poussin sums of Fourier-Chebyshev rational integral operators and approximations to Poisson integrals on the segment ⋮ The Riesz-Zygmund sums of Fourier-Chebyshev rational integral operators and their approximation properties ⋮ Unnamed Item ⋮ Conjugate rational Fourier-Chebyshev operator and its approximation properties

Cites Work

• Asymptotic behavior of best approximations of classes of Poisson integrals of functions from \(H_\omega\)
• An approximation of \(| \sin \,x|\) by rational Fourier series
• An estimate of the remainder of the Fourier series for differentiable functions
• Solution of the Kolmogorov-Nikol'skii problem for the Poisson integrals of continuous functions
• Approximation of Classes of Analytic Functions by de la Vallée-Poussin Sums
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