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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 $L_p$, 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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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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