Advertisement

Uniqueness of the best approximation in mean of vector-valued functions

  • A. L. Garkavi
Article
  • 36 Downloads

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    D. Jackson, “Note on a class of polynomials of approximation,” Trans. Am. Math. Soc.,22, 320–326 (1921).Google Scholar
  2. 2.
    S. I. Zukhovitskii and S. B. Stechkin, “On the approximation of abstract functions with values in a Banach space,” Dokl. Akad. Nauk SSSR,106, No. 5, 773–776 (1957).Google Scholar
  3. 3.
    J. Singer, “Sur la meilleure approximation des fonctions abstraites continues a valeurs dans un espace de Banach,” Rev. Roumaine Math. Pures Appl.,2, 245–262 (1957).Google Scholar
  4. 4.
    V. A. Koshcheev, “Systems of continuous vector-valued functions of a given. Chebyshev rank,” Mat. Zametki,33, No. 1, 31–40 (1982).Google Scholar
  5. 5.
    B. R. Kripke and T. J. Rivlin, “Approximation in the metric of L1(t, Μ), “ Trans. Am. Math. Soc.,119, 101–122 (1965).Google Scholar
  6. 6.
    A. Kroo, “Best L1-approximation of vector-valued functions,” Acta Math. Acad. Sci. Hung.,39, 303–310 (1982).Google Scholar
  7. 7.
    J. Singer, Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Springer-Verlag, Berlin (1970).Google Scholar
  8. 8.
    N. Bourbaki, Topological Vector Spaces, Addison-Wesley.Google Scholar
  9. 9.
    M. G. Krein and A. A. Nudel'man, Markov's Problem of Moments and Extremal Problems [in Russian], Nauka, Moscow (1973).Google Scholar
  10. 10.
    V. K. Dzyadyk, Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow (1977).Google Scholar
  11. 11.
    Kim-Pin Lim, “Note on the uniqueness of best approximation in C1(X),” Tamkang J. Math.,5, No. 1, 81–85 (1974).Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • A. L. Garkavi
    • 1
  1. 1.Moscow Engineering-Construction InstituteUSSR

Personalised recommendations