Equiconvergence of expansions in multiple Fourier series and in fourier integrals with "lacunary sequences of partial sums"

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• 作者：I. L. Bloshanskii ; D. A. Grafov
• 关键词：multiple Fourier series ; multiple Fourier integrals ; convergence almost everywhere ; lacunary sequence
• 刊名：Mathematical Notes
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：99
• 期：1-2
• 页码：196-209
• 全文大小：879 KB
• 参考文献：1.A. Zygmund, Trigonometric Series (Cambridge Univ. Press, Cambridge, 1960), Vol. 2.
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  5.I. L. Bloshanskii and D. A. Grafov, “Equiconvergence of expansions in multiple trigonometric Fourier series and integrals in the case of a “lacunary sequence of partial sums”,” Dokl. Akad. Nauk 450 (3), 260–263 (2013) [Dokl.Math. 87 (3), 296–299 (2013)].MathSciNet MATH
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• 作者单位：I. L. Bloshanskii (1)
  D. A. Grafov (1)
  
  1. Moscow State Regional University, Moscow, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1573-8876

文摘

We investigate the equiconvergence on T N = [−π, π) N of expansions in multiple trigonometric Fourier series and in the Fourier integrals of functions f ∈ L _p (T N ) and g ∈ L _p (R N ), p > 1, N ≥ 3, g(x) = f(x) on T N , in the case where the “partial sums” of these expansions, i.e., S _n (x; f) and J _α(x; g), respectively, have “numbers” n ∈ Z N and α ∈ R N (n _j = [α _j ], j = 1,..., N, [t] is the integral part of t ∈ R1) containing N − 1 components which are elements of “lacunary sequences.”

Keywords multiple Fourier series, multiple Fourier integrals convergence almost everywhere lacunary sequence Original Russian Text © I. L. Bloshanskii, D. A. Grafov, 2016, published in Matematicheskie Zametki, 2016, Vol. 99, No. 2, pp. 186–200.