Sharp inequalities for approximations of classes of periodic convolutions by odd-dimensional subspaces of shifts

DOI10.1134/S0001434609030250zbMath1211.41003MaRDI QIDQ1033960

O. L. Vinogradov

Publication date: 10 November 2009

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

zbMATH Keywords

splineinequalityJackson inequalityperiodic convolutionFavard-Akhiezer-Krein inequality

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Inequalities for sums, series and integrals (26D15) Convolution, factorization for one variable harmonic analysis (42A85) Rate of convergence, degree of approximation (41A25) Spline approximation (41A15) Approximation by positive operators (41A36) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (13)

Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions ⋮ Sharp estimates for the mean-square approximations of convolution classes by shift spaces on the axis ⋮ Fourier analysis in spaces of shifts ⋮ Sharp Jackson type inequalities for spline approximation on the axis ⋮ Optimal subspaces for mean square approximation of classes of differentiable functions on a segment ⋮ Estimates for functionals with a known finite set of moments in terms of deviations of operators constructed with the use of the Steklov averages and finite differences ⋮ Estimates of functionals by the second modulus of continuity of even derivatives ⋮ New recursive representations for the Favard constants with application to multiple singular integrals and summation of series ⋮ Sharp estimates for mean square approximations of classes of differentiable periodic functions by shift spaces ⋮ Sharp constants for approximations of convolution classes with an integrable kernel by spaces of shifts ⋮ Estimates for functionals with a known, finite set of moments, in terms of moduli of continuity, and behavior of constants, in the Jackson-type inequalities ⋮ Classes of convolutions with a singular family of kernels: Sharp constants for approximation by spaces of shifts ⋮ Sharp estimates for mean square approximations of classes of periodic convolutions by spaces of shifts

Cites Work

• Approximation of convolution classes
• Inequalities for upper bounds of functionals
• Exact error bound of approximation by interpolating splines in \(L\)-metric on the classes \(W^r_p(1\leq p<\infty)\) of periodic functions
• On extremal subspaces for classes of functions defined by kernels that do not increase oscillation
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