Approximation of the Lebesgue constant of the Fourier operator by a logarithmic-fractional-rational function

DOI10.3103/S1066369X23110099zbMATH Open1542.41017MaRDI QIDQ6549001

I. A. Shakirov

Publication date: 3 June 2024

Published in: Russian Mathematics (Search for Journal in Brave)

zbMATH Keywords

asymptotic formulaapproximation errorextreme problemfractional rational functionLebesgue constant of Fourier operatortwo-way estimation of Lebesgue constant

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Best constants in approximation theory (41A44)

Cites Work

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• Inequalities and asymptotic expansions for the constants of Landau and Lebesgue
• Some sharp estimates of the constants of Landau and Lebesgue
• Über die Lebesgueschen Konstanten bei den Fourierschen Reihen.
• Sur les singularités de la série de \textit{Fourier} des fonctions continues.
• \textit{Lebesgue}sche Konstanten und divergente \textit{Fourier}reihen.
• Unified treatment of several asymptotic expansions concerning some mathematical constants
• The constants of Landau and Lebesgue.
• About the optimal replacement of the Lebesque constant Fourier operator by a logarithmic function
• On optimal approximations of the norm of the Fourier operator by a family of logarithmic functions
• Approximation of the Lebesgue constant of the Fourier operator by a logarithmic function
• Asymptotic approximations of integrals
• Note on Lebesgue's Constants in the Theory of Fourier Series

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