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Mat. Sb. (N.S.), 1972, Volume 89(131), Number 3(11), Pages 355–365 (Mi msb3238)  

This article is cited in 4 scientific papers (total in 4 papers)

On the convergence of series of weakly multiplicative systems of functions

V. F. Gaposhkin


Abstract: A system of measurable functions $\{\varphi_k\}$ defined on a measurable space is called weakly multiplicative if it satisfies the relations
$$ \int_X\varphi_{k_1}\varphi_{k_2}…\varphi_{k_p} d\mu=0\quad(\forall p\geqslant2, k_1<k_2<…<k_p). $$

In this paper the convergence in the metric of $L_p$ and a.e. is investigated for series of weakly multiplicative system of functions. One of the results is: {\it If $\{\varphi_k\}$ is weakly multiplicative and $\sup_k\|\varphi_k\|_p\leqslant M$ for some $p>2,$ then any series $\sum c_k\varphi_k$ with coefficients in $l_2$ converges unconditionally a.e. and in $L_p$}. For $p=2n$, instead of weak multiplicativity it is sufficient to require the condition $\int_X\varphi_{k_1}…\varphi_{k_{2n}} d\mu=0$ ($\forall k_1<…<k_{2n}$).
Bibliography: 13 titles.

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English version:
Mathematics of the USSR-Sbornik, 1972, 18:3, 361–372

Bibliographic databases:

UDC: 517.522
MSC: Primary 42A60; Secondary 60G45, 60G50
Received: 25.10.1971

Citation: V. F. Gaposhkin, “On the convergence of series of weakly multiplicative systems of functions”, Mat. Sb. (N.S.), 89(131):3(11) (1972), 355–365; Math. USSR-Sb., 18:3 (1972), 361–372

Citation in format AMSBIB
\Bibitem{Gap72}
\by V.~F.~Gaposhkin
\paper On the convergence of series of weakly multiplicative systems of functions
\jour Mat. Sb. (N.S.)
\yr 1972
\vol 89(131)
\issue 3(11)
\pages 355--365
\mathnet{http://mi.mathnet.ru/msb3238}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=334315}
\zmath{https://zbmath.org/?q=an:0249.42013}
\transl
\jour Math. USSR-Sb.
\yr 1972
\vol 18
\issue 3
\pages 361--372
\crossref{https://doi.org/10.1070/SM1972v018n03ABEH001818}


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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. A. S. Krantsberg, “On divergent Fourier series in orthogonal systems”, Math. USSR-Sb., 22:4 (1974), 547–560  mathnet  crossref  mathscinet  zmath
    2. M. Longnecker, R. J. Serfling, “Moment inequalities for S n under general dependence restrictions, with applications”, Z Wahrscheinlichkeitstheorie verw Gebiete, 43:1 (1978), 1  crossref  mathscinet  zmath
    3. P. A. Yaskov, “On asymptotic constancy of diagonal elements of a random orthogonal projection”, Russian Math. Surveys, 69:4 (2014), 755–756  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. A. I. Rubinshtein, “Ob odnom mnozhestve slabo multiplikativnykh sistem”, Matem. zametki, 105:3 (2019), 471–475  mathnet  crossref  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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