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Mat. Zametki, 1972, Volume 12, Issue 1, Pages 13–17 (Mi mz9841)  

This article is cited in 3 scientific papers (total in 4 papers)

On the Cantor–Lebesgue theorem for double trigonometric series

S. B. Stechkin

V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR

Abstract: Suppose that on some measurable set $E\subset\mathbf{T}^2$, $\mu(E)>2/3$,
$$ A_\nu(x)=\sum_{n_1^2+n_2^2=\nu}c_{n_1,n_2}e^{2\pi i(n_1x_1+n_2x_2)}\to0\qquad(\nu\to\infty). $$
Then
$$ \sum_{n_1^2+n_2^2=\nu}|c_{n_1,n_2}|^2\to0\qquad(\nu\to\infty). $$


Full text: PDF file (427 kB)

English version:
Mathematical Notes, 1972, 12:1, 441–443

Bibliographic databases:

UDC: 517.5
Received: 23.02.1972

Citation: S. B. Stechkin, “On the Cantor–Lebesgue theorem for double trigonometric series”, Mat. Zametki, 12:1 (1972), 13–17; Math. Notes, 12:1 (1972), 441–443

Citation in format AMSBIB
\Bibitem{Ste72}
\by S.~B.~Stechkin
\paper On the Cantor--Lebesgue theorem for double trigonometric series
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 1
\pages 13--17
\mathnet{http://mi.mathnet.ru/mz9841}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=316970}
\zmath{https://zbmath.org/?q=an:0253.42020}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 1
\pages 441--443
\crossref{https://doi.org/10.1007/BF01094387}


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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. B. I. Golubov, “On convergence of Riesz spherical means of multiple Fourier series”, Math. USSR-Sb., 25:2 (1975), 177–197  mathnet  crossref  mathscinet  zmath
    2. Sh. A. Alimov, V. A. Il'in, E. M. Nikishin, “Convergence problems of multiple trigonometric series and spectral decompositions. I”, Russian Math. Surveys, 31:6 (1976), 29–86  mathnet  crossref  mathscinet  zmath
    3. M. I. Dyachenko, “Some problems in the theory of multiple trigonometric series”, Russian Math. Surveys, 47:5 (1992), 103–171  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. O. V. Besov, V. M. Buchstaber, A. G. Vitushkin, A. A. Gonchar, S. V. Konyagin, L. D. Kudryavtsev, S. M. Nikol'skii, S. P. Novikov, Yu. S. Osipov, A. Yu. Popov, V. A. Sadovnichii, A. F. Sidorov, Yu. N. Subbotin, S. A. Telyakovskii, P. L. Ul'yanov, N. I. Chernykh, “Sergei Borisovich Stechkin (obituary)”, Russian Math. Surveys, 51:6 (1996), 1007–1014  mathnet  crossref  crossref  mathscinet  adsnasa  isi
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