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Mat. Zametki, 1972, Volume 11, Issue 5, Pages 473–480 (Mi mz9813)  

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

Sets of absolute convergence of double trigonometric series

R. A. Avetisyan

M. V. Lomonosov Moscow State University

Abstract: We obtain a sufficient condition for a set of plane measure zero to be a set of absolute convergence (an A.C.-set) for a double trigonometric series. Specifically, let $y=f(x)$ ($0\leqslant x\leqslant2\pi$) be a smooth curve and let $\bigvee\limits_0^{2\pi}\ln|f'(x)|<\infty$. Then, any set of positive linear measure lying on this curve is an A.C.-set.

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English version:
Mathematical Notes, 1972, 11:5, 289–293

Bibliographic databases:

UDC: 517.5
Received: 25.06.1971

Citation: R. A. Avetisyan, “Sets of absolute convergence of double trigonometric series”, Mat. Zametki, 11:5 (1972), 473–480; Math. Notes, 11:5 (1972), 289–293

Citation in format AMSBIB
\Bibitem{Ave72}
\by R.~A.~Avetisyan
\paper Sets of absolute convergence of double trigonometric series
\jour Mat. Zametki
\yr 1972
\vol 11
\issue 5
\pages 473--480
\mathnet{http://mi.mathnet.ru/mz9813}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=303213}
\zmath{https://zbmath.org/?q=an:0246.42017|0234.42010}
\transl
\jour Math. Notes
\yr 1972
\vol 11
\issue 5
\pages 289--293
\crossref{https://doi.org/10.1007/BF01158639}


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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. R. A. Avetisyan, “On sets of absolute convergence”, Math. USSR-Sb., 38:2 (1981), 245–254  mathnet  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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