Advertisement

Ukrainian Mathematical Journal

, Volume 50, Issue 11, pp 1649–1658 | Cite as

The best L 1-approximations of classes of functions defined by differential operators in terms of generalized splines from these classes

  • V. F. Babenko
  • Leis Azar
Article

Abstract

For classes of periodic functions defined by constraints imposed on the L 1-norm of the result of action of differential operators with constant coefficients and real spectrum on these functions, we determine the exact values of the best L 1-approximations by generalized splines from the classes considered.

Keywords

Differential Operator Periodic Function Real Root Linear Normed Space Real Spectrum 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. N. Kolmogorov, “On the best approximation of functions from a given functional class,” in: Mathematics and Mechanics. Selected Works [in Russian], Nauka, Moscow (1985), pp. 186–189.Google Scholar
  2. 2.
    V. N. Konovalov, “Estimates of Kolmogorov widths for classes of differentiable periodic functions,” Mat. Zametki, 35, No. 3, 369–380 (1984).zbMATHMathSciNetGoogle Scholar
  3. 3.
    V. M. Tikhomirov, Some Problems in the Theory of Approximation [in Russian], Moscow University, Moscow (1976).Google Scholar
  4. 4.
    V. F. Babenko, “Approximation in the mean under restrictions imposed on the derivatives of approximating functions,” in: Problems in Analysis and the Theory of Approximation [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1989), pp. 9–18.Google Scholar
  5. 5.
    V. F. Babenko, “Best L 1 -approximations of classes W1r by splines from W1r,” Ukr. Mat. Zh., 46, No. 10, 1418–1421 (1994).CrossRefMathSciNetGoogle Scholar
  6. 6.
    V. F. Babenko, “On the best uniform approximations by splines under restrictions imposed on their derivatives,” Mat. Zametki, 50, No. 6, 24–30 (1991).MathSciNetGoogle Scholar
  7. 7.
    V. F. Babenko, “On the best L1-approximations by splines under restrictions imposed on their derivatives,” Mat. Zametki, 51, No. 5, 12–19 (1992).MathSciNetGoogle Scholar
  8. 8.
    N. P. Korneichuk, Exact Constants in the Theory of Approximation [in Russian], Nauka, Moscow (1987).Google Scholar
  9. 9.
    V. F. Babenko, “Extremal problems in the theory of approximation and a permutation inequality,” Dokl. Akad. Nauk SSSR, 290, No. 5, 1033–1036 (1986).MathSciNetGoogle Scholar
  10. 10.
    V. F. Babenko, “Approximation of classes of functions determined by the modulus of continuity,” Dokl. Akad. Nauk SSSR, 298, No. 6, 1296–1299 (1988).Google Scholar
  11. 11.
    N. P. Korneichuk, V. F. Babenko, and A. A. Ligun, Extremal Properties of Polynomials and Splines [in Russian], Naukova Dumka, Kiev (1992).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1998

Authors and Affiliations

  • V. F. Babenko
    • 1
  • Leis Azar
    • 1
  1. 1.Dnepropetrovsk UniversityDnepropetrovsk

Personalised recommendations