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On the best linear approximation methods and the widths of certain classes of analytic functions

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Abstract

We discuss the best linear approximation methods in the Hardy spaceH q q≥1, for classes of analytic functions studied by N. Ainulloev; these are generalizations (in a certain sense) of function sets introduced by L. V. Taikov. The exact values of their linear and Gelfandn-widths are obtained. The exact values of the Kolmogorov and Bernsteinn-widths of classes of analytic (in |z|<1) functions whose boundaryK-functionals are majorized by a prescribed functions are also obtained.

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References

  1. A. Pinkusn-Widths in Approximation Theory, Berlin (1985).

  2. S. D. Fisher and M. I. Stessin, “Then-width of the unit ball ofH q,”J. Approx. Theory,67, No. 3, 347–356 (1991).

    Article  MATH  Google Scholar 

  3. Yu. A. Farkov, “The widths of the Hardy and Bergman classes in a ball from ℂn,”Uspekhi Mat. Nauk [Russian Math. Surveys],45, No. 5, 197–198 (1990).

    Google Scholar 

  4. S. B. Vakarchuk, “Best linear approximation methods and the widths of classes of analytic functions on the disk,”Mat. zametki [Math. Notes],57, No. 1, 30–39 (1995).

    Google Scholar 

  5. A. V. Taikov, “The widths of some classes of analytic functions,”Mat. Zametki, [Math. Notes],22, No. 2, 285–295 (1977).

    Google Scholar 

  6. N. Ainulloev, “The widths of classes of analytic functions on the unit disk”, in:Geometric Problems in Function and Set Theory [in Russian], Kalinin (1986), pp. 91–101.

  7. V. M. Tikhomirov,Some Problems in Approximation Theory [in Russian], Izd. Moskov. Univ., Moscow (1976).

    Google Scholar 

  8. J. Bergh and J. Löfstrom,Interpolation Spaces. An Introduction, Springer-Verlag, Berlin-Heidelberg-New York (1976).

    MATH  Google Scholar 

  9. P. Oswald, “On some approximation properties of real Hardy spaces (0<p≤1),”J. Approx. Theory,40, No. 1, 45–65 (1984).

    Article  MATH  Google Scholar 

  10. L. L. Schumaker,Spline Functions. Basic Theory, Wiley, New York (1981).

    MATH  Google Scholar 

  11. A. Zygmund,Trigonometric Series, Vol. 1, Cambridge Univ. Press, Cambridge (1959).

    MATH  Google Scholar 

  12. N. I. Shikhaliev, “Bernstein-Markov type inequalities for analytic functions,”Dokl. Akad. Nauk Azerbaidzh. SSR,31, No. 8, 9–14 (1975).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Institute for Geotechnical Mechanics, National Academy of Sciences of Ukraine, Dnepropetrovsk

    S. B. Vakarchuk

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  1. S. B. Vakarchuk
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Translated fromMatermaticheskie Zametki, Vol. 65, No. 2, pp. 186–193, February, 1999.

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Vakarchuk, S.B. On the best linear approximation methods and the widths of certain classes of analytic functions. Math Notes 65, 153–158 (1999). https://doi.org/10.1007/BF02679811

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  • DOI: https://doi.org/10.1007/BF02679811

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