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Matematicheskie Zametki, 1997, Volume 61, Issue 4, Pages 583–595
DOI: https://doi.org/10.4213/mzm1537 (Mi mzm1537) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Convergence of multiple Fourier series for functions of bounded variation

S. A. Telyakovskiia, V. N. Temlyakovb

a Steklov Mathematical Institute, Russian Academy of Sciences
b University of South Carolina
Full-text PDF (227 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm1537
Abstract: For functions of bounded variation in the sense of Hardy, we consider the pointwise convergence of the partial sums of Fourier series over a given sequence of bounded sets in the space of harmonics. We obtain sufficient conditions for convergence; necessary and sufficient conditions are obtained for the case in which these sets are convex with respect to each coordinate direction. The Pringsheim convergence of Fourier series in this problem was established by Hardy.
Received: 22.12.1995
English version:
Mathematical Notes, 1997, Volume 61, Issue 4, Pages 484–494
DOI: https://doi.org/10.1007/BF02354993
Bibliographic databases:
Document Type: Article
UDC: 517.518.475
Language: Russian
Citation: S. A. Telyakovskii, V. N. Temlyakov, “Convergence of multiple Fourier series for functions of bounded variation”, Mat. Zametki, 61:4 (1997), 583–595; Math. Notes, 61:4 (1997), 484–494
Citation in format AMSBIB
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\paper Convergence of multiple Fourier series for functions of bounded variation
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\jour Math. Notes
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  • https://www.mathnet.ru/eng/mzm1537
  • https://doi.org/10.4213/mzm1537
  • https://www.mathnet.ru/eng/mzm/v61/i4/p583
    • This publication is cited in the following 4 articles:
    1. K. I. Oskolkov, “The Series $\sum\sum\frac{e^{2\pi imnx}}{mn}$ and a Problem of Chowla”, Proc. Steklov Inst. Math., 248 (2005), 197–215  mathnet  mathscinet  zmath
    2. K. I. Oskolkov, “On a Result of Telyakovskii and Multiple Hilbert Transforms with Polynomial Phases”, Math. Notes, 74:2 (2003), 232–244  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. M. I. Dyachenko, “Two-dimensional Waterman classes and $u$-convergence of Fourier series”, Sb. Math., 190:7 (1999), 955–972  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. S. A. Telyakovskii, “Certain Special Multiple Sine Series”, Proc. Steklov Inst. Math., 227 (1999), 293–304  mathnet  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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