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

DOI10.3103/S1066369X14070032zbMath1309.30032OpenAlexW2143651385MaRDI QIDQ2262907

M. R. Langarshoev, Mirgand Shabozovich Shabozov, Sergei B. Vakarchuk

Publication date: 17 March 2015

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

Full work available at URL: https://doi.org/10.3103/s1066369x14070032

zbMATH Keywords

approximation by entire functionsfunctions on \(\mathbb R\)

Mathematics Subject Classification ID

Approximation in the complex plane (30E10) Special classes of entire functions of one complex variable and growth estimates (30D15)

Related Items (7)

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 ⋮ Unnamed Item ⋮ 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 ⋮ Generalized characteristics of smoothness and some extreme problems of the approximation theory of functions in the space \(L_2(\mathbb{R})\). II ⋮ On estimates in \(L_2(\mathbb{R} )\) of mean \(\nu \)-widths of classes of functions defined via the generalized modulus of continuity of \(\omega_\mathcal{M} \) ⋮ Generalized characteristics of smoothness and some extreme problems of the approximation theory of functions in the space \(L_2(\mathbb{R})\). I ⋮ On generalized characteristics of smoothness of functions and on average $\nu$-widths in the space $L_2(\mathbb{R})$

Cites Work

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• On some extremal problems of approximation theory of functions on the real axis. I
• Widths of classes of periodic differentiable functions in the space \(L_{2} [0, 2\pi\)]
• Best mean square approximations by entire functions of finite degree on a straight line and exact values of mean widths of functional classes
• MEAN DIMENSION, WIDTHS, AND OPTIMAL RECOVERY OF SOBOLEV CLASSES OF FUNCTIONS ON THE LINE

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