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Mat. Sb., 2015, Volume 206, Number 7, Pages 55–94 (Mi msb8424)  

This article is cited in 5 scientific papers (total in 5 papers)

Convergence of Fourier series in classical systems

L. N. Galoyan, M. G. Grigoryan, A. Kh. Kobelyan

Yerevan State University, Armenia

Abstract: The following results are proved:
  • there exists an integrable function such that any subsequence of the Cesàro means of negative order of the Fourier series of this function diverges almost everywhere;
  • the values of an arbitrary integrable function can be changed on a set (independent of this function) of arbitrarily small measure so that the Fourier series with respect to both the Franklin system and the Haar system of the ‘modified’ function will be absolutely convergent almost everywhere on $[0,1]$;
  • there exists a continuous function which features an unremovable absolute divergence.

Bibliography: 47 titles.

Keywords: Fourier series, classical systems, Cesàro means, almost everywhere convergence, convergence in the norm, absolute convergence.

Funding Agency Grant Number
State Committee on Science of the Ministry of Education and Science of the Republic of Armenia SCS 13-1A313
This research was carried out with the financial support of the State Committee on Science of the Republic of Armenia (project no. SCS 13-1A313).


DOI: https://doi.org/10.4213/sm8424

Full text: PDF file (770 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2015, 206:7, 941–979

Bibliographic databases:

Document Type: Article
UDC: 517.51
MSC: 42A20
Received: 23.09.2014

Citation: L. N. Galoyan, M. G. Grigoryan, A. Kh. Kobelyan, “Convergence of Fourier series in classical systems”, Mat. Sb., 206:7 (2015), 55–94; Sb. Math., 206:7 (2015), 941–979

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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. L. N. Galoyan, R. G. Melikbekyan, “On the almost everywhere convergence of negative order Cesaro means of Fourier–Walsh series”, Uch. zapiski EGU, ser. Fizika i Matematika, 2016, no. 1, 64–66  mathnet
    2. L. N. Galoyan, R. G. Melikbekyan, “Behavior of the Fourier–Walsh coefficients of a corrected function”, Siberian Math. J., 57:3 (2016), 505–512  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. Grigoryan M.G., Kobelyan A.Kh., “On Behavior of Fourier Coefficients and Uniform Convergence of Fourier Series in the Haar System”, Adv. Oper. Theory, 3:4 (2018), 781–793  crossref  mathscinet  zmath  isi  scopus
    4. M. G. Grigoryan, A. A. Sargsyan, “The Fourier–Faber–Schauder series unconditionally divergent in measure”, Siberian Math. J., 59:5 (2018), 835–842  mathnet  crossref  crossref  isi
    5. M. G. Grigoryan, “Ob absolyutnoi skhodimosti ryadov Fure–Khaara v metrike $L^p(0,1)$, $0<p<1$”, Issledovaniya po lineinym operatoram i teorii funktsii. 46, Zap. nauchn. sem. POMI, 467, POMI, SPb., 2018, 34–54  mathnet
  • Математический сборник Sbornik: Mathematics (from 1967)
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