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Matematicheskie Zametki, 2021, Volume 109, Issue 2, Pages 206–218
DOI: https://doi.org/10.4213/mzm12747 (Mi mzm12747) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Uniqueness Theorems for Multiple Franklin Series Converging over Rectangles

G. G. Gevorkyan, L. A. Akopyan

Yerevan State University
Full-text PDF (530 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm12747
Abstract: It is proved that if a multiple series in the Franklin system converges in the sense of Pringsheim everywhere, except, perhaps, on a set that is a Cartesian product of sets of measure zero, to an everywhere finite integrable function, then it is the Fourier–Franklin series of this function. A uniqueness theorem is also proved for multiple Franklin series whose rectangular partial sums at each point have a sequential limit.
Keywords: Franklin system, multiple series, uniqueness theorem.
Funding agency Grant number
State Committee on Science of the Ministry of Education and Science of the Republic of Armenia 18T-1A074
This work was supported by the State Committee on Science of the Republic of Armenia (grant no. 18T-1A074).
Received: 09.04.2020
Revised: 17.07.2020
English version:
Mathematical Notes, 2021, Volume 109, Issue 2, Pages 208–217
DOI: https://doi.org/10.1134/S0001434621010247
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: G. G. Gevorkyan, L. A. Akopyan, “Uniqueness Theorems for Multiple Franklin Series Converging over Rectangles”, Mat. Zametki, 109:2 (2021), 206–218; Math. Notes, 109:2 (2021), 208–217
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm/v109/i2/p206
    • This publication is cited in the following 1 articles:
    1. M. G. Plotnikov, “Uniqueness sets of positive measure for the trigonometric system”, Izv. Math., 86:6 (2022), 1179–1203  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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