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Polygonal Dirichlet Kernels and growth of Lebesgue constants

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Literature cited

  1. V. A. I1'in, “Problems of localization and convergence for Fourier series with respect to the fundamental systems of eigenfunctions of the Laplace operator,” Usp. Mat. Nauk,23, No. 2, 61–120 (1968).

    Google Scholar 

  2. K. I. Babenko, On the Mean Convergence of Multiple Fourier Series and the Asymptotic of the Dirichlet Kernel of Spherical Means [in Russian], Preprint No. 52, Inst. Prikl. Mat. Akad. Nauk SSSR, Moscow (1971).

    Google Scholar 

  3. V. A. Yudin, “Behavior of the Lebesgue constants,” Mat. Zametki,17, No. 3, 401–405 (1975).

    Google Scholar 

  4. V. A. Yudin, “Lower bound for Lebesgue constants,” Mat. Zametki,25, No. 1, 119–122 (1979).

    Google Scholar 

  5. É. S. Belinskii, “Behavior of Lebesgue constants for some methods of summation of multiple Fourier series,” in: Metric Questions in the Theory of Functions and Mappings [in Russian], G. D. Surorov and V. I. Belyi (eds.), Naukova Dumka, Kiev (1977), pp. 19–39.

    Google Scholar 

  6. A. N. Podkorytov, “The order of growth of the Lebesgue constants of Fourier sums over polyhedra,” Vestn. Leningr. Gos. Univ., No. 7, 110–111 (1982).

    Google Scholar 

  7. S. P. Baiborodov, “The Lebesgue constants of polygons,” Mat. Zametki,32, No. 6, 817–822 (1982).

    Google Scholar 

  8. A. Ya. Khinchin, Continued Fractions [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  9. A. N. Podkorytov, “On the Lebesgue constants of double Fourier series,” Vestn. Leningr. Gos. Univ., No. 7, 79–84 (1977).

    Google Scholar 

  10. A. A. Yudin and V. A. Yudin, “Discrete embedding theorems and Lebesgue constants,” Mat. Zametki,22, No. 3, 381–394 (1977).

    Google Scholar 

  11. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press (1971).

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Authors and Affiliations

  1. Vladimir Pedagogical Institute, USSR

    A. A. Yudin & V. A. Yudin

  2. Moscow Energy Institute, USSR

    A. A. Yudin & V. A. Yudin

Authors
  1. A. A. Yudin
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  2. V. A. Yudin
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Translated from Matematicheskie Zametki, Vol. 37, No. 2, pp. 220–236, February, 1985.

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Yudin, A.A., Yudin, V.A. Polygonal Dirichlet Kernels and growth of Lebesgue constants. Mathematical Notes of the Academy of Sciences of the USSR 37, 124–135 (1985). https://doi.org/10.1007/BF01156757

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  • DOI: https://doi.org/10.1007/BF01156757

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