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Mat. Sb., 2012, Volume 203, Number 6, Pages 35–62 (Mi msb7851)  

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

Some properties of the sum of the moduli of the terms of a grouped trigonometric series

A. S. Belov

Ivanovo State University

Abstract: For a trigonometric series grouped in a certain way and such that the coefficients are monotonic in each of the groups, the absolute convergence and properties of the sums of moduli of the terms thereof are examined. Necessary and sufficient conditions for this sum to lie in $L^p_{2\pi}$-spaces, $p\in[1,\infty]$, are obtained, and upper and lower bounds in terms for the coefficients of the series are established.
Bibliography: 9 titles.

Keywords: absolute convergence, grouped trigonometric series.

DOI: https://doi.org/10.4213/sm7851

Full text: PDF file (625 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2012, 203:6, 798–825

Bibliographic databases:

UDC: 517.518.4
MSC: 42A20, 42A32
Received: 04.02.2011

Citation: A. S. Belov, “Some properties of the sum of the moduli of the terms of a grouped trigonometric series”, Mat. Sb., 203:6 (2012), 35–62; Sb. Math., 203:6 (2012), 798–825

Citation in format AMSBIB
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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. S. A. Telyakovskii, “Series formed by the moduli of blocks of terms of trigonometric series. A survey”, J. Math. Sci., 209:1 (2015), 152–158  mathnet  crossref  mathscinet  elib
    2. S. A. Telyakovskii, “On the series of absolute values of blocks of trigonometric series”, Proc. Steklov Inst. Math., 284 (2014), 235–243  mathnet  crossref  crossref  isi  elib
    3. V. P. Zastavnyi, A. S. Levadnaya, “Integriruemost so stepennym vesom summ iz modulei blokov trigonometricheskikh ryadov”, Tr. IMM UrO RAN, 23, no. 3, 2017, 125–133  mathnet  crossref  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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