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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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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
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
•  Number of views: This page: 216 Full text: 70 References: 41 First page: 1

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