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Izvestiya: Mathematics, 2020, Volume 84, Issue 4, Pages 816–828
DOI: https://doi.org/10.1070/IM8862 (Mi im8862) 		 
This article is cited in 7 scientific papers (total in 7 papers)

General orthonormal systems and absolute convergence

V. Sh. Tsagareishvili

Tbilisi Ivane Javakhishvili State University
English version PDF (423 kB) Citations (7)
References:
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DOI: https://doi.org/10.1070/IM8862
Abstract: We study problems of the absolute convergence of Fourier series of differentiable functions with respect to general orthonormal systems (ONS). We obtain results which show that under certain conditions on functions in the ONS, the Fourier series of an arbitrary function in a certain differentiability class is absolutely convergent. We finally note that our results cannot be improved.
Keywords: orthonormal system, absolute convergence of Fourier series, Fourier coefficients, function of bounded variation.
Received: 12.09.2018
Revised: 04.11.2019
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2020, Volume 84, Issue 4, Pages 208–220
DOI: https://doi.org/10.4213/im8862
Bibliographic databases:
Document Type: Article
UDC: 517.521
MSC: 42A16, 42A20
Language: English
Original paper language: Russian
Citation: V. Sh. Tsagareishvili, “General orthonormal systems and absolute convergence”, Izv. RAN. Ser. Mat., 84:4 (2020), 208–220; Izv. Math., 84:4 (2020), 816–828
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/im8862
  • https://doi.org/10.1070/IM8862
  • https://www.mathnet.ru/eng/im/v84/i4/p208
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:241
    Russian version PDF:26
    English version PDF:11
    References:34
    First page:8
     
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