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Mat. Sb., 2016, Volume 207, Number 12, Pages 110–123 (Mi msb8707)  

This article is cited in 3 scientific papers (total in 3 papers)

On nonequivalence of the $\mathrm{C}$- and $\mathrm{QC}$-norms in the space of trigonometric polynomials

A. O. Radomskii

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: A nontrivial lower bound for the quantity $\sup_{t\in L}\|t\|_{\mathrm{QC}}/\|t\|_{\infty}$ is obtained for a subspace $L$ of $ \mathrm{T}(2^{m}-1)$ which satisfies a certain dimension condition.
Bibliography: 8 titles.

Keywords: trigonometric polynomials, Fejér kernels, Rademacher functions.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.4213/sm8707

Full text: PDF file (484 kB)
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English version:
Sbornik: Mathematics, 2016, 207:12, 1729–1742

Bibliographic databases:

Document Type: Article
UDC: 517.518
MSC: Primary 42A05; Secondary 46E999
Received: 31.03.2016 and 24.04.2016

Citation: A. O. Radomskii, “On nonequivalence of the $\mathrm{C}$- and $\mathrm{QC}$-norms in the space of trigonometric polynomials”, Mat. Sb., 207:12 (2016), 110–123; Sb. Math., 207:12 (2016), 1729–1742

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/msb8707
  • https://doi.org/10.4213/sm8707
  • http://mi.mathnet.ru/eng/msb/v207/i12/p110

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

    This publication is cited in the following articles:
    1. A. O. Radomskii, “On the Sidon inequality for trigonometric polynomials”, St. Petersburg Math. J., 29:4 (2018), 643–656  mathnet  crossref  mathscinet  isi  elib
    2. A. O. Radomskii, “On approximation characteristics of some classes of functions of small smoothness”, Siberian Math. J., 59:3 (2018), 486–493  mathnet  crossref  crossref  isi  elib
    3. A. O. Radomskii, “Some properties of the space of quasi-continuous functions”, Russian Math. Surveys, 73:6 (2018), 1119–1121  mathnet  crossref  crossref  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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