On rational Abel-Poisson means on a segment and approximations of Markov functions

MaRDI QIDQ6669648

E. A. Rovba, P. G. Patseika

Publication date: 22 January 2025

Published in: Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika (Search for Journal in Brave)

zbMATH Keywords

Markov functionsasymptotic estimatesbest approximationsexact constantsAbel-Poisson meansrational integral operatorsChebyshev-Markov algebraic fractions

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Trigonometric approximation (42A10) Best approximation, Chebyshev systems (41A50) Convergence and absolute convergence of Fourier and trigonometric series (42A20)

Cites Work

• Best approximations by rational functions with a fixed number of poles
• Best rational approximation to Markov functions
• Sur la détermination d'une classe de fonctions analytiques par leurs valeurs dans un ensemble donné de points.
• On the orthogonal functions and a new formula of interpolation.
• Uniform approximations of Stieltjes functions by orthogonal projection on the set of rational functions
• Rational approximations of functions of Markov-Stieltjes type in Hardy spaces \(H^p\), \(0 < p \leq \infty\)
• Rational approximation of Markov functions generated by Borelean power-type measures
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