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 Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 4, Pages 675–707 (Mi izv1269)

The structure and geometry of maximal sets of convergence and unbounded divergence almost everywhere of multiple Fourier series of functions in $L_1$ equal to zero on a given set

I. L. Bloshanskii

Abstract: The precise structure and geometry of maximal sets of convergence and unbounded divergence almost everywhere (a.e.) of Fourier series of functions in the class $L_1(T^N)$, $N\geqslant1$, $T^N[0,2\pi]^N$, and vanishing on a given measurable set $E$ is found (in the case $N\geqslant2$ this is done for both rectangular and square summation).
Bibliography: 21 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1990, 35:1, 1–35

Bibliographic databases:

UDC: 517.5
MSC: Primary 42B05; Secondary 42A63

Citation: I. L. Bloshanskii, “The structure and geometry of maximal sets of convergence and unbounded divergence almost everywhere of multiple Fourier series of functions in $L_1$ equal to zero on a given set”, Izv. Akad. Nauk SSSR Ser. Mat., 53:4 (1989), 675–707; Math. USSR-Izv., 35:1 (1990), 1–35

Citation in format AMSBIB
\Bibitem{Blo89} \by I.~L.~Bloshanskii \paper The structure and geometry of maximal sets of convergence and unbounded divergence almost everywhere of multiple Fourier series of functions in~$L_1$ equal to zero on a~given set \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1989 \vol 53 \issue 4 \pages 675--707 \mathnet{http://mi.mathnet.ru/izv1269} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1018743} \zmath{https://zbmath.org/?q=an:0701.42008} \transl \jour Math. USSR-Izv. \yr 1990 \vol 35 \issue 1 \pages 1--35 \crossref{https://doi.org/10.1070/IM1990v035n01ABEH000684} 

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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. M. I. Dyachenko, “Some problems in the theory of multiple trigonometric series”, Russian Math. Surveys, 47:5 (1992), 103–171
2. S. K. Bloshanskaya, I. L. Bloshanskii, “Generalized localization for the multiple Walsh–Fourier series of functions in $L_p$, $p\geqslant 1$”, Sb. Math., 186:2 (1995), 181–196
3. 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
4. S. K. Bloshanskaya, I. L. Bloshanskii, T. Yu. Roslova, “Generalized localization for the double trigonometric Fourier series and the Walsh–Fourier series of functions in $L\log^+L\log^+\log^+L$”, Sb. Math., 189:5 (1998), 657–682
5. O. K. Ivanova, “Majorant estimates for partial sums of multiple Fourier series from Orlicz spaces that vanish on some set”, Math. Notes, 65:6 (1999), 694–700
6. I. L. Bloshanskii, “A Criterion for Weak Generalized Localization in the Class $L_1$ for Multiple Trigonometric Series from the Viewpoint of Isometric Transformations”, Math. Notes, 71:4 (2002), 464–476
7. I. L. Bloshanskii, T. A. Matseevich, “A Weak Generalize Localization of Multiple Fourier Series of Continuous Functions with a Certain Module of Continuity”, Journal of Mathematical Sciences, 155:1 (2008), 31–46
8. I. L. Bloshanskii, O. V. Lifantseva, “Weak Generalized Localization for Multiple Fourier Series Whose Rectangular Partial Sums Are Considered with Respect to Some Subsequence”, Math. Notes, 84:3 (2008), 314–327
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