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Ukrainian Mathematical Journal

, Volume 46, Issue 7, pp 891–902 | Cite as

Exact values of meann-widths for the classes of functions analytic in the upper half plane in the Hardy space

  • S. B. Vakarchuk
Article
  • 21 Downloads

Abstract

In the Hardy spaceH2 + 2 of functions analytic in the upper half plane such that
$$\sup \left\{ {\int\limits_\mathbb{R} {|f(x + iy)|^2 dx: 0< y< \infty } } \right\}< \infty ,$$
we determine meanN-widths and find their exact values for numerous classes of functions.

Keywords

Hardy Space Half Plane Numerous Classis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Ding Zung and G. G. Magaril-Il'yaev, “Problems of Bernstein and Favard types and the mean ɛ-dimensionality of some function classes,”Dokl. Akad. Nauk SSSR,249, No. 4, 783–786 (1979).Google Scholar
  2. 2.
    G. G. Magaril-Il'yaev, “Mean dimensionalities and widths of some classes of functions given on a line,”Dokl. Akad. Nauk SSSR,318, No. 1, 35–38 (1991).Google Scholar
  3. 3.
    F. G. Nasibov, “To the theory of approximations by entire functions,” in:Approximation of Functions by Linear Operators. Convergence of Fourier Series [in Russian], Azerbaijan Institute of Oil and Chemistry, Baku (1987), pp. 26–45.Google Scholar
  4. 4.
    V. E. Maiorov, “On the widths of classes of functions given on a line,”Mat. Zametki,34, No. 3, 355–366 (1983).Google Scholar
  5. 5.
    J. Garnett,Bounded Analytic Functions [Russian translation], Mir, Moscow (1984).Google Scholar
  6. 6.
    A. Pinkus,N-Widths in Approximation Theory, Springer-Verlag, Berlin (1985).Google Scholar
  7. 7.
    V. M. Tikhomirov,Some Problems of Approximation Theory [in Russian], Moscow University, Moscow (1976).Google Scholar
  8. 8.
    S. B. Vakarchuk, “On the widths of some classes of analytic functions in the Hardy spaceH 2Ukr. Mat. Zh.,41, No. 6, 799–803 (1989).Google Scholar
  9. 9.
    V. V. Shalayev, “On the widths in L2 of some classes of differentiable functions defined in terms of the moduli of continuity of higher orders,”Ukr. Mat. Zh.,43, No. 1, 125–129 (1991).Google Scholar
  10. 10.
    P. M. Tamrazov,Smoothness and Polynomial Approximations [in Russian], Naukova Dumka, Kiev (1975).Google Scholar
  11. 11.
    F. D. Gakhov and Yu. I. Cherskii,Equations of Convolution Type [in Russian], Nauka, Moscow (1978).Google Scholar
  12. 12.
    A. F. Timan,Theory of Approximation of Real-Valued Functions [in Russian], Fizmatgiz, Moscow (1960).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • S. B. Vakarchuk
    • 1
  1. 1.Institute of Geotechnic MechanicsUkrainian Academy of SciencesDnepropetrovsk

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