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Mat. Sb., 1992, Volume 183, Number 10, Pages 3–12 (Mi msb1077)  

This article is cited in 2 scientific papers (total in 2 papers)

The generalized Bari theorem for the Walsh system

N. N. Kholshchevnikova


Abstract: For Walsh series in the Paley arrangement the author proves a generalized Bari theorem on the union of sets of uniqueness, from which it follows in particular that the union of two $\mathcal U$-sets, one of which is simultaneously an $F_\sigma$-set and a $G_\delta$-set, is a $\mathcal U$-set, and the union of two disjoint $\mathcal U$-sets of type $G_\delta$ is again a $\mathcal U$-set. It is shown that the last two assertions hold for sets of uniqueness of those classes of series for which the principle of localization of the kernel holds.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1994, 77:1, 139–147

Bibliographic databases:

UDC: 517.5
MSC: Primary 42C10; Secondary 42C25
Received: 12.12.1991

Citation: N. N. Kholshchevnikova, “The generalized Bari theorem for the Walsh system”, Mat. Sb., 183:10 (1992), 3–12; Russian Acad. Sci. Sb. Math., 77:1 (1994), 139–147

Citation in format AMSBIB
\Bibitem{Kho92}
\by N.~N.~Kholshchevnikova
\paper The generalized Bari theorem for the~Walsh system
\jour Mat. Sb.
\yr 1992
\vol 183
\issue 10
\pages 3--12
\mathnet{http://mi.mathnet.ru/msb1077}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1202789}
\zmath{https://zbmath.org/?q=an:0789.42022|0771.42017}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1994SbMat..77..139K}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 77
\issue 1
\pages 139--147
\crossref{https://doi.org/10.1070/SM1994v077n01ABEH003433}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1994MZ10900009}


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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. V. A. Skvortsov, N. N. Kholshchevnikova, “$M$-sets for three classes of series in the Faber–Schauder system”, Math. Notes, 64:5 (1998), 634–645  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. N. N. Kholshchevnikova, “Theorems on unions of $U$-sets”, Math. Notes, 67:5 (2000), 657–664  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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