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On exact order estimates of N-widths of classes of functions analytic in a simply connected domain

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Abstract

In the spaces E q(Ω), 1 < q < ∞, introduced by Smirnov, we obtain exact order estimates of projective and spectral n-widths of the classes W r E p(Ω) and W r E p(Ω)Ф in the case where p and q are not equal. We also indicate extremal subspaces and operators for the approximative values under consideration.

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References

  1. S. B. Vakarchuk, “On widths of some classes of analytic functions. I,” Ukr. Mat. Zh., 44, No. 3, 324–333 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  2. S. B. Vakarchuk, “On widths of some classes of analytic functions. II,” Ukr. Mat. Zh., 44, No. 8, 1135–1138 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  3. S. B. Vakarchuk, “Analytic splines and widths of functional classes,” Dokl Akad. Nauk. Ukr. SSR, No. 5, 7–11 (1994).

  4. A. Pinkus, N-Widths in Approximation Theory, Springer, Berlin 1985.

    MATH  Google Scholar 

  5. S. B. Vakarchuk, “Diameters of classes of analytic functions,” in: Optimal Recovery. Proceedings of the Second International Symposium on Optimal Algorithms (Varna, May 29-June 2, 1989), Nova, New York (1992), pp. 297–310.

    Google Scholar 

  6. Yu. A. Farkov, “On widths of some classes of analytic functions,” Usp. Mat. Nauk, 39, No. 1, 161–162 (1984).

    MATH  MathSciNet  Google Scholar 

  7. V. L. Oleinik, “Estimates of widths of compact sets of analytic functions in L p with weight,” Vestn. Leningrad. Univ., No. 7, 47–51 (1975).

  8. S. D. Fischer and C. A. Micchelli, “The n-widths of sets of analytic functions,” Duke Math. J., 47, No. 4, 789–801 (1980).

    Article  MathSciNet  Google Scholar 

  9. S. B. Vakarchuk, “On exact estimates of widths of classes of analytic functions of many complex variables,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 7, 3–6 (1993).

  10. é. M. Galeev, “On spectral widths of finite-dimensional sets,” Vestn. Mosk. Univ., Ser. I. Mat., Mekh., 41–44 (1988).

  11. I. N. Glazman and Yu. I. Lyubich, Finite-Dimensional Linear Analysis [in Russian], Nauka, Moscow 1969.

    Google Scholar 

  12. P. K. Suetin, Series in Faber Polynomials [in Russian], Nauka, Moscow 1984.

    Google Scholar 

  13. I. N. Vekua, Generalized Analytic Functions [in Russian], Fizmatgiz, Moscow 1952.

    Google Scholar 

  14. V. M. Tikhomirov, Some Problems in the Theory of Approximation [in Russian], Moscow University, Moscow (1976).

    Google Scholar 

  15. S. Ya. Al’per, “On approximation of analytic functions from the class E p in the mean,” in: Studies in Contemporary Problems in the Theory of Functions of a Complex Variable [in Russian], Fizmatgiz, Moscow (1960), pp. 273–286.

    Google Scholar 

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  1. S. B. Vakarchuk
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Vakarchuk, S.B. On exact order estimates of N-widths of classes of functions analytic in a simply connected domain. Ukr Math J 48, 601–606 (1996). https://doi.org/10.1007/BF02390619

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  • DOI: https://doi.org/10.1007/BF02390619

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