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Matematicheskie Zametki, 1970, Volume 7, Issue 4, Pages 403–410 (Mi mzm9523)  
This article is cited in 4 scientific papers (total in 5 papers)

On the set of sums of a functional series

E. M. Nikishin

M. V. Lomonosov Moscow State University
Full-text PDF (837 kB) Citations (5)
Abstract: A positive answer is given to one of Banach's problems on the set of sums of a functional series for various permutations of its terms. The problem is solved subject to one restricting condition, that $\sum_{n=1}^\infty f_n^2(x)<\infty$ almost everywhere in $[0, 1]$.
Received: 10.11.1969
English version:
Mathematical Notes, 1970, Volume 7, Issue 4, Pages 243–247
DOI: https://doi.org/10.1007/BF01151696
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: E. M. Nikishin, “On the set of sums of a functional series”, Mat. Zametki, 7:4 (1970), 403–410; Math. Notes, 7:4 (1970), 243–247
Citation in format AMSBIB
\Bibitem{Nik70}
\by E.~M.~Nikishin
\paper On the set of sums of a functional series
\jour Mat. Zametki
\yr 1970
\vol 7
\issue 4
\pages 403--410
\mathnet{http://mi.mathnet.ru/mzm9523}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=271574}
\zmath{https://zbmath.org/?q=an:0202.35301|0194.37401}
\transl
\jour Math. Notes
\yr 1970
\vol 7
\issue 4
\pages 243--247
\crossref{https://doi.org/10.1007/BF01151696}
Linking options:
  • https://www.mathnet.ru/eng/mzm9523
  • https://www.mathnet.ru/eng/mzm/v7/i4/p403
    • This publication is cited in the following 5 articles:
    1. A. G. Vitushkin, A. A. Gonchar, B. S. Kashin, A. I. Kostrikin, S. M. Nikol'skii, S. P. Novikov, P. L. Ul'yanov, L. D. Faddeev, “Evgenii Mikhailovich Nikishin (obituary)”, Russian Math. Surveys, 42:5 (1987), 153–160  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. S. A. Chobanyan, “Structure of the set of sums of a conditionally convergent series in a normed space”, Math. USSR-Sb., 56:1 (1987), 49–62  mathnet  crossref  mathscinet  zmath
    3. P. A. Kornilov, “On the linearity of the set of sums of a series of functions”, Russian Math. Surveys, 37:2 (1982), 217–218  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. P. A. Kornilov, “On rearrangements of conditionally convergent series of functions”, Math. USSR-Sb., 41:4 (1982), 495–510  mathnet  crossref  mathscinet  zmath
    5. E. M. Nikishin, “Rearrangements of function series”, Math. USSR-Sb., 14:2 (1971), 267–280  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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