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Sbornik: Mathematics, 2015, Volume 206, Issue 7, Pages 941–979
DOI: https://doi.org/10.1070/SM2015v206n07ABEH004484 (Mi sm8424) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Convergence of Fourier series in classical systems

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

Yerevan State University, Armenia
English version PDF (724 kB) Citations (12)
References:
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DOI: https://doi.org/10.1070/SM2015v206n07ABEH004484
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).
Received: 23.09.2014
Russian version:
Matematicheskii Sbornik, 2015, Volume 206, Number 7, Pages 55–94
DOI: https://doi.org/10.4213/sm8424
Bibliographic databases:
Document Type: Article
UDC: 517.51
MSC: 42A20
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2015v206n07ABEH004484
  • https://www.mathnet.ru/eng/sm/v206/i7/p55
    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:252
    English version PDF:15
    References:72
    First page:50
     
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