O. L. Vinogradov, “Sharp Inequalities for Approximations of Classes of Periodic Convolutions by Odd-Dimensional Subspaces of Shifts”, Mat. Zametki, 85:4 (2009), 569–584; Math. Notes, 85:4 (2009), 544

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Matematicheskie Zametki, 2009, Volume 85, Issue 4, Pages 569–584
DOI: https://doi.org/10.4213/mzm4162 (Mi mzm4162)

This article is cited in 14 scientific papers (total in 14 papers)

Sharp Inequalities for Approximations of Classes of Periodic Convolutions by Odd-Dimensional Subspaces of Shifts

O. L. Vinogradov

Saint-Petersburg State University

Full-text PDF (599 kB) Citations (14)

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DOI: https://doi.org/10.4213/mzm4162

Abstract: Sharp Akhiezer–Krein–Favard-type inequalities for classes of periodic convolutions with kernels that do not increase oscillation are obtained. A large class of approximating odd-dimensional subspaces constructed from uniform shifts of one function with extremal widths is specified. As a corollary, sharp Jackson-type inequalities for the second-order modulus of continuity are derived.

Keywords: Akhiezer–Krein–Favard inequality, periodic convolution, Jackson inequality, second-order modulus of continuity, the space

L_{p}

$L_p$ , Sobolev class, spline.

Received: 05.05.2005
Revised: 15.05.2008

English version:
Mathematical Notes, 2009, Volume 85, Issue 4, Pages 544–557
DOI: https://doi.org/10.1134/S0001434609030250

Bibliographic databases:

UDC: 517.5

Language: Russian

Citation: O. L. Vinogradov, “Sharp Inequalities for Approximations of Classes of Periodic Convolutions by Odd-Dimensional Subspaces of Shifts”, Mat. Zametki, 85:4 (2009), 569–584; Math. Notes, 85:4 (2009), 544–557

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm4162

https://doi.org/10.4213/mzm4162

https://www.mathnet.ru/eng/mzm/v85/i4/p569

This publication is cited in the following 14 articles:

A. Yu. Ulitskaya, “Sharp estimates for the mean-square approximations of convolution classes by shift spaces on the axis”, Siberian Math. J., 64:1 (2023), 157–173
A. Yu. Ulitskaya, “FOURIER ANALYSIS IN SPACES OF SHIFTS”, J Math Sci, 266:4 (2022), 603
O. L. Vinogradov, “Classes of convolutions with a singular family of kernels: Sharp constants for approximation by spaces of shifts”, St. Petersburg Math. J., 32:2 (2021), 233–260
A. Yu. Ulitskaya, “Sharp estimates for mean square approximations of classes of periodic convolutions by spaces of shifts”, St. Petersburg Math. J., 32:2 (2021), 349–369
Vinogradov O.L., Ulitskaya A.Yu., “Optimal Subspaces For Mean Square Approximation of Classes of Differentiable Functions on a Segment”, Vestn. St Petersb. Univ.-Math., 53:3 (2020), 270–281
Vinogradov O.L. Ulitskaya A.Yu., “Sharp Estimates For Mean Square Approximations of Classes of Differentiable Periodic Functions By Shift Spaces”, Vestnik St. Petersburg Univ. Math., 51:1 (2018), 15–22
O. L. Vinogradov, “Sharp constants for approximations of convolution classes with an integrable kernel by spaces of shifts”, St. Petersburg Math. J., 30:5 (2019), 841–867
Gladkaya A.V. Vinogradov O.L., “Sharp Jackson type inequalities for spline approximation on the axis”, Anal. Math., 43:1 (2017), 27–47
O. L. Vinogradov, “Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions”, Siberian Math. J., 58:2 (2017), 190–204
Norifumi Shioda, “RNA toxicity and RAN translation in repeat expansion disorders”, Folia Pharmacologica Japonica, 150:3 (2017), 165
Gocheva-Ilieva S.G. Feschiev I.H., “New Recursive Representations for the Favard Constants with Application to Multiple Singular Integrals and Summation of Series”, Abstract Appl. Anal., 2013, 523618
O. L. Vinogradov, V. V. Zhuk, “Estimates of functionals by the second moduli of continuity of even derivatives”, J. Math. Sci. (N. Y.), 202:4 (2014), 526–540
O. L. Vinogradov, V. V. Zhuk, “Estimates for functional with a known finite set of moments in terms of moduli of continuity and behaviour of constants in the Jackson-type inequalities”, St. Petersburg Math. J., 24:5 (2013), 691–721
O. L. Vinogradov, V. V. Zhuk, “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”, J. Math. Sci. (N. Y.), 184:6 (2012), 679–698

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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