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Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 1, Pages 83–91 (Mi timm1031)  

This article is cited in 4 scientific papers (total in 4 papers)

An estimate of an optimal argument in the sharp multidimensional Jackson–Stechkin $L_2$-inequality

D. V. Gorbachev

Tula State University

Abstract: An estimate of an optimal argument in the sharp Jackson–Stechkin inequality in the space $L_2(\mathbb R^n)$ is proved in the case of a generalized modulus of continuity; its special case is the classical modulus of continuity. Similar statements hold for the torus $\mathbb T^n$. The obtained results agree with Chernykh's classical one-dimensional theorems and refine some results by S. N. Vasil'ev, A. I. Kozko, and N. I. Rozhdestvenskii.

Keywords: best approximation, generalized modulus of continuity, sharp multidimensional Jackson–Stechkin inequality.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, 288, suppl. 1, 70–78

Bibliographic databases:

UDC: 517.5
Received: 09.01.2014

Citation: D. V. Gorbachev, “An estimate of an optimal argument in the sharp multidimensional Jackson–Stechkin $L_2$-inequality”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 1, 2014, 83–91; Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 70–78

Citation in format AMSBIB
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\paper An estimate of an optimal argument in the sharp multidimensional Jackson--Stechkin $L_2$-inequality
\serial Trudy Inst. Mat. i Mekh. UrO RAN
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\vol 20
\issue 1
\pages 83--91
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2015
\vol 288
\issue , suppl. 1
\pages 70--78
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. I. Ivanov, A. V. Ivanov, “Optimal Arguments in the Jackson–Stechkin Inequality in $L_2(\mathbb{R}^d)$ with Dunkl Weight”, Math. Notes, 96:5 (2014), 666–677  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. S. B. Vakarchuk, “Best Polynomial Approximations and Widths of Classes of Functions in the Space $L_2$”, Math. Notes, 103:2 (2018), 308–312  mathnet  crossref  crossref  isi  elib
    3. V. Ivanov, A. Ivanov, “Generalized Logan's problem for entire functions of exponential type and optimal argument in Jackson's inequality in $L_2(\mathbb{R}^3)$”, Acta. Math. Sin.-English Ser., 34:10 (2018), 1563–1577  crossref  mathscinet  zmath  isi  scopus
    4. S. B. Vakarchuk, “Ob otsenkakh v $L_2(\mathbb{R})$ srednikh $\nu$-poperechnikov klassov funktsii, opredelennykh pri pomoschi obobschennogo modulya nepreryvnosti $\omega_{\mathcal{M}}$”, Matem. zametki, 106:2 (2019), 198–211  mathnet  crossref  elib
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