S. V. Bochkarev, “Absolute convergence of Fourier series with respect to bounded systems”, Mat. Zametki, 15:3 (1974), 363–370; Math. Notes, 15:3 (1974), 207

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Matematicheskie Zametki, 1974, Volume 15, Issue 3, Pages 363–370 (Mi mzm7356)

This article is cited in 7 scientific papers (total in 7 papers)

Absolute convergence of Fourier series with respect to bounded systems

S. V. Bochkarev

Steklov Mathematical Institute, Academy of Sciences of the USSR

Full-text PDF (400 kB) Citations (7)

Abstract: In this paper we prove that for the piecewise-linear unit jump approximation the sum of the moduli of the Fourier coefficients with respect to an arbitrary complete orthonormal system, which is totally bounded, has, when averaged over sections, a lower bound of order

\log N

$\log N$ , where

N^{- 1}

$N^{-1}$ is the approximation step.

Received: 25.12.1972

English version:
Mathematical Notes, 1974, Volume 15, Issue 3, Pages 207–211
DOI: https://doi.org/10.1007/BF01438371

Bibliographic databases:

Document Type: Article

UDC: 517.5

Language: Russian

Citation: S. V. Bochkarev, “Absolute convergence of Fourier series with respect to bounded systems”, Mat. Zametki, 15:3 (1974), 363–370; Math. Notes, 15:3 (1974), 207–211

Citation in format AMSBIB

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\by S.~V.~Bochkarev

\paper Absolute convergence of Fourier series with respect to bounded systems

\jour Mat. Zametki

\yr 1974

\vol 15

\issue 3

\pages 363--370

\mathnet{http://mi.mathnet.ru/mzm7356}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=358211}

\zmath{https://zbmath.org/?q=an:0304.42011|0302.42011}

\transl

\jour Math. Notes

\yr 1974

\vol 15

\issue 3

\pages 207--211

\crossref{https://doi.org/10.1007/BF01438371}

Linking options:

https://www.mathnet.ru/eng/mzm7356

https://www.mathnet.ru/eng/mzm/v15/i3/p363

This publication is cited in the following 7 articles:

S. V. Bochkarev, “An abstract Kolmogorov theorem, and an application to metric spaces and topological groups”, Sb. Math., 209:11 (2018), 1575–1602
A. V. Meleshkina, “Fourier Coefficients of Characteristic Functions of Intervals with Respect to a Complete Orthonormal System Bounded in $L^p([0,1])$ , $2<p<\infty$ ”, Math. Notes, 97:4 (2015), 647–651
S. V. Bochkarev, “de la Vallée-Poussin means of Fourier series for the quadratic spectrum and for spectra with power-like density”, Russian Math. Surveys, 69:1 (2014), 119–152
S. V. Bochkarev, “A Generalization of Kolmogorov's Theorem to Biorthogonal Systems”, Proc. Steklov Inst. Math., 260 (2008), 37–49
S. V. Bochkarev, “Multiplicative Inequalities for the $L_1$ Norm: Applications in Analysis and Number Theory”, Proc. Steklov Inst. Math., 255 (2006), 49–64
B. S. Kashin, “Lower Bounds for $n$ -Term Approximations”, Math. Notes, 70:4 (2001), 574–576
B. S. Kashin, “Remarks on estimating the Lebesgue functions of an orthonormal system”, Math. USSR-Sb., 35:1 (1979), 57–62

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

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