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Izvestiya: Mathematics, 2020, Volume 84, Issue 5, Pages 829–844
DOI: https://doi.org/10.1070/IM8889 (Mi im8889) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Uniqueness theorems for one-dimensional and double Franklin series

G. G. Gevorkyan

Yerevan State University
English version PDF (525 kB) Citations (3)
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DOI: https://doi.org/10.1070/IM8889
Abstract: The paper contains two main results. First we describe one-dimensional Franklin series converging everywhere except possibly on a finite set to an everywhere-finite integrable function. Second we establish a class of subsets of $[0, 1]^2$ with the following property. If a double Franklin series converges everywhere except on this set to an everywhere-finite integrable function, then it is the Fourier–Franklin series of this function. In particular, all countable sets are in this class.
Keywords: uniqueness theorem, $U$-set, Vallée–Poussin set, Franklin system, double series.
Funding agency Grant number
State Committee on Science of the Ministry of Education and Science of the Republic of Armenia 18T–1A074
This paper was written with the financial support of SCS MES RA under the grant 18T–1A074.
Received: 12.12.2018
Revised: 06.05.2020
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2020, Volume 84, Issue 5, Pages 3–19
DOI: https://doi.org/10.4213/im8889
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: 42C10
Language: English
Original paper language: Russian
Citation: G. G. Gevorkyan, “Uniqueness theorems for one-dimensional and double Franklin series”, Izv. RAN. Ser. Mat., 84:5 (2020), 3–19; Izv. Math., 84:5 (2020), 829–844
Citation in format AMSBIB
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  • https://doi.org/10.1070/IM8889
  • https://www.mathnet.ru/eng/im/v84/i5/p3
    • This publication is cited in the following 3 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:388
    Russian version PDF:59
    English version PDF:34
    References:48
    First page:17
     
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