On some extremal problems of approximation theory of functions on the real axis. I

DOI10.1007/S10958-012-1113-8zbMath1268.41023OpenAlexW4253225258MaRDI QIDQ1945783

Sergei B. Vakarchuk

Publication date: 9 April 2013

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

Full work available at URL: https://doi.org/10.1007/s10958-012-1113-8

zbMATH Keywords

widthmodulus of continuitybest approximationJackson-type inequalityFourier transformationmajorantclass of functionsentire function of the exponential typereal axisaverage \(\nu\)-width

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17)

Related Items (6)

Exact constants in Jackson-type inequalities for the best mean square approximation in \(L_2(\mathbb{R})\) and exact values of mean \(\nu\)-widths of the classes of functions ⋮ On the estimates of the values of various widths of classes of functions of two variables in the weight space \(L_{2, \gamma } ( \mathbb{R}^2)\), \(\gamma = \exp ( - x^2 - y^2)\) ⋮ On the moduli of continuity and fractional-order derivatives in the problems of best mean-square approximation by entire functions of the exponential type on the entire real axis ⋮ On the best mean square approximations by entire functions of exponential type in \(L_2(\mathbb R)\) and mean \(\nu\)-widths of some functional classes ⋮ Generalized characteristics of smoothness and some extreme problems of the approximation theory of functions in the space \(L_2(\mathbb{R})\). II ⋮ Generalized characteristics of smoothness and some extreme problems of the approximation theory of functions in the space \(L_2(\mathbb{R})\). I

Cites Work

• Jackson-type inequalities and widths of function classes in \(L_{2}\)
• Über die beste Annäherung von Funktionen einer gegebenen Funktionenklasse
• Exact constants in Jackson-type inequalities for L 2-approximation on an axis
• Best mean square approximations by entire functions of finite degree on a straight line and exact values of mean widths of functional classes
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