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Izv. Vyssh. Uchebn. Zaved. Mat., 2012, Number 1, Pages 67–71 (Mi ivm8421)  

This article is cited in 1 scientific paper (total in 1 paper)

Coefficients of convergent multiple Haar series

M. G. Plotnikov

Chair of Higher Mathematics and Physics, The Vereshchagin Vologda State Dairy Farming Academy, Molochnoye, Vologda, Russia

Abstract: It is well-known that if a multiple trigonometric series almost everywhere converges in the square or restricted rectangular sense to a finite function, then its coefficients grow slower than any exponential function. In this paper we prove the existence of a multiple Haar series that converges in the square or restricted rectangular sense to a finite function and contains a subsequence of coefficients that grows faster than any sequence defined an advance. Moreover, we show that for such series conditions of the Arutyunyan–Talalyan type can be violated at some points.

Keywords: Haar system, multiple Haar series, convergence in the square sense, convergence in the restricted rectangular sense, Cantor–Lebesgue type theorems.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:1, 61–65

Bibliographic databases:

UDC: 517.518+517.521
Received: 20.12.2010

Citation: M. G. Plotnikov, “Coefficients of convergent multiple Haar series”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 1, 67–71; Russian Math. (Iz. VUZ), 56:1 (2012), 61–65

Citation in format AMSBIB
\Bibitem{Plo12}
\by M.~G.~Plotnikov
\paper Coefficients of convergent multiple Haar series
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2012
\issue 1
\pages 67--71
\mathnet{http://mi.mathnet.ru/ivm8421}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2975920}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2012
\vol 56
\issue 1
\pages 61--65
\crossref{https://doi.org/10.3103/S1066369X12010094}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84862653490}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. G. Plotnikov, “Coefficients of convergent multiple Walsh-Paley series”, Sb. Math., 203:9 (2012), 1295–1309  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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