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Mat. Zametki, 1970, Volume 7, Issue 4, Pages 403–410 (Mi mz9523)  

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

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 $[0, 1]$.

Full text: PDF file (837 kB)

English version:
Mathematical Notes, 1970, 7:4, 243–247

Bibliographic databases:

UDC: 517.5
Received: 10.11.1969

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/mz9523}
\mathscinet{http://www.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}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. M. Nikishin, “Rearrangements of function series”, Math. USSR-Sb., 14:2 (1971), 267–280  mathnet  crossref  mathscinet  zmath
    2. P. A. Kornilov, “On rearrangements of conditionally convergent series of functions”, Math. USSR-Sb., 41:4 (1982), 495–510  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. 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
    5. 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
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