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Ukrainian Mathematical Journal

, Volume 66, Issue 7, pp 986–993 | Cite as

Optimal Recovery of n-Linear Functionals According to Linear Information

  • V. F. Babenko
  • M. S. Gun’ko
  • A. A. Rudenko
Article
  • 51 Downloads

We determine the optimal linear information and the optimal procedure of its application for the recovery of n-linear functionals on the sets of special form from a Hilbert space.

Keywords

Hilbert Space English Translation Linear Normed Space Optimal Recovery Proper 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.
    V. F. Babenko, “On the best application of linear functionals for the approximation of bilinear functionals,” in: Investigations of the Contemporary Problems of Summation and Approximation of Functions and Their Applications [in Russian], Dnepropetrovsk (1979), pp. 3–5.Google Scholar
  2. 2.
    V. F. Babenko, “Approximate computation of scalar products,” Ukr. Mat. Zh., 40, No. 1, 15–21 (1988); English translation: Ukr. Math. J., 40, No. 1, 11–16 (1988).Google Scholar
  3. 3.
    V. F. Babenko and A. A. Rudenko, “Optimal reconstruction of convolutions and scalar products of functions from various classes,” Ukr. Mat. Zh., 43, No. 10, 1305–1310 (1991); English translation: Ukr. Math. J., 43, No. 10, 1214–1219 (1991).Google Scholar
  4. 4.
    V. F. Babenko and A. A. Rudenko, “Optimal reconstruction of scalar products of functions from various classes,” in: Theory of Functions and Approximations [in Russian], Saratov (1991), pp. 17–22.Google Scholar
  5. 5.
    V. F. Babenko and A. A. Rudenko, “Optimal reconstruction of scalar products of functions in the classes of functions defined by differential operators,” in: Approximation of Functions and Summation of Series [in Russian], Dnepropetrovsk (1992), pp. 8–13.Google Scholar
  6. 6.
    V. F. Babenko and A. A. Rudenko, “On the optimal renewal of bilinear functionals in linear normed spaces,” Ukr. Mat. Zh., 49, No. 6, 828–831 (1997); English translation: Ukr. Math. J., 49, No. 6, 925–929 (1997).Google Scholar
  7. 7.
    V. F. Babenko, M. S. Gun’ko, and A. A. Rudenko, “On the optimal recovery of bilinear functionals according to linear information,” Visn. Dnipropetr. Univ., Ser. Mat., Issue 17, 11–17 (2012).Google Scholar
  8. 8.
    V. F. Babenko, M. S. Gun’ko, and A. A. Rudenko, “On the optimal recovery of n-linear functionals according to linear information,” Visn. Dnipropetr. Univ., Ser. Mat., Issue 18, 16–25 (2013).Google Scholar
  9. 9.
    I. M. Sobol’, Multidimensional Quadrature Formulas and Haar Functions [in Russian], Nauka, Moscow (1969).Google Scholar
  10. 10.
    G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge University Press, Cambridge (1934).Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • V. F. Babenko
    • 1
  • M. S. Gun’ko
    • 1
  • A. A. Rudenko
    • 1
  1. 1.Gonchar Dnepropetrovsk National UniversityDnepropetrovskUkraine

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