Ukrainian Mathematical Journal

, Volume 42, Issue 6, pp 740–744 | Cite as

The best polynomial approximation of functions analytic in the unit circle

  • S. B. Vakarchuk
Brief Communications

Abstract

In the Banach space ℬ(p,q,λ), studied by M. I. Gvaradze, we establish a relation between the best polynomial approximation of an entire transcendental function and such important characteristics as its order of growth and its type.

Keywords

Banach Space Unit Circle Polynomial Approximation Transcendental Function Entire Transcendental Function 
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.

Literature cited

  1. 1.
    M. I. Gvaradze, “On the spaces ℬ (p, q. λ) of analytic functions,” Soobshch. Akad. Nauk GruzSSR,77, No. 2, 273–275 (1975).Google Scholar
  2. 2.
    M. I. Gvaradze, On a Class of Spaces of Analytic Functions, Dissertation for a Candidate of the Physicomathematical Sciences, Tbilisi (1975).Google Scholar
  3. 3.
    G. A. Oniani, “The approximation of analytic functions by linear means,” Soobshch. Akad. Nauk GruzSSR,87, No. 1, 21–24 (1977).Google Scholar
  4. 4.
    A. R. Reddy, “A contribution to best approximation in the L2 norm,” J. Approx. Theory,11, No. 1, 110–117 (1974).Google Scholar
  5. 5.
    I. I. Ibragimov and N. P. Shikhaliev, “On the best polynomial approximation in a space of of analytic functions,” Dokl. Akad. Nauk SSSR,227, No. 2, 280–283 (1976).Google Scholar
  6. 6.
    I. I. Ibragimov and N. P. Shikhaliev, “On the best approximation in the mean of analytic functions in the space Ap(¦z¦ < 1),” in: Special Questions in the Theory of Functions [in Russian], Vol. 1, Izdat. Elm, Baku (1977), pp. 84–96.Google Scholar
  7. 7.
    E. T. Whittaker and G. N. Watson, A Course in Modern Analysis. Part 2. Transcendental Functions [Russian trnaslation], Fizmatgiz, Moscow (1963).Google Scholar
  8. 8.
    V. I. Smirnov and N. A. Lebedev, Constructive Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1964).Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • S. B. Vakarchuk
    • 1
  1. 1.Institute of Geotechnical MechanicsAcademy of Sciences of the USSRDnepropetrovsk

Personalised recommendations