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Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 3, Pages 685–705 (Mi izv2159)  

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

Equiconvergence of expansions in a multiple Fourier series and Fourier integral for summation over squares

I. L. Bloshanskii


Abstract: In this work there are constructed a function $f(\overline x)\in L_1([-\pi,\pi]^2)$ such that the difference between the Fourier series expansion and the Fourier integral expansion for summation over squares diverges almost everywhere on $\{[-\pi,\pi]^2\}$, and a function $f(\overline x)\in L_p([-\pi,\pi]^N)$, $p>1$, $N\geqslant2$, for which the difference diverges at a point.
Bibliography: 5 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:3, 652–671

Bibliographic databases:

UDC: 517.5
MSC: Primary 42A92, 42A20; Secondary 40B05
Received: 13.12.1974

Citation: I. L. Bloshanskii, “Equiconvergence of expansions in a multiple Fourier series and Fourier integral for summation over squares”, Izv. Akad. Nauk SSSR Ser. Mat., 40:3 (1976), 685–705; Math. USSR-Izv., 10:3 (1976), 652–671

Citation in format AMSBIB
\Bibitem{Blo76}
\by I.~L.~Bloshanskii
\paper Equiconvergence of expansions in a~multiple Fourier series and Fourier integral for summation over squares
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1976
\vol 40
\issue 3
\pages 685--705
\mathnet{http://mi.mathnet.ru/izv2159}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=415196}
\zmath{https://zbmath.org/?q=an:0348.42005}
\transl
\jour Math. USSR-Izv.
\yr 1976
\vol 10
\issue 3
\pages 652--671
\crossref{https://doi.org/10.1070/IM1976v010n03ABEH001726}


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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. I. L. Bloshanskii, O. K. Ivanova, T. Yu. Roslova, “Generalized localization and equiconvergence of expansions in double trigonometric series and in the Fourier integral for functions from $L(\ln^+L)^2$”, Math. Notes, 60:3 (1996), 324–327  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. I. L. Bloshanskii, D. A. Grafov, “Equiconvergence of Expansions in Multiple Fourier Series and in Fourier Integrals with “Lacunary Sequences of Partial Sums””, Math. Notes, 99:2 (2016), 196–209  mathnet  crossref  crossref  mathscinet  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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