Journal of Mathematical Sciences

, Volume 92, Issue 1, pp 3630–3634 | Cite as

Bernstein and Gelfand widths of certain classes of analytic functions. II

  • O. G. Parfenov


The Gelfand widths of the unit ball of H2(ν) (the weighted Hardy space) with respect to the metric of the space L(Tr) are considered (here Tr is the circle of radius r centered at the origin), as well as the Bernstein widths of the unit ball of H with respect to the metric of the space L2(Tr, μ). Asymptotic formulas for the widths in question are established for arbitrary measures ν, μ. Bibliography: 5 titles.


Lebesgue Measure Unit Ball Lower Estimate Asymptotic Formula Blaschke Product 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    O. G. Parfenov, “Gelfand and Bernstein widths of some classes of continuous functions,Zap. Nauchn. Semin. POMI,217, 112–129 (1994).MATHGoogle Scholar
  2. 2.
    O. G. Parfenov, “The widths of a certain class of analytic functions,”Mat. Sb.,117, 279–285 (1982).MATHMathSciNetGoogle Scholar
  3. 3.
    W. Grenander and G. Szegö,Toeplitz Forms and Their Applications [Russian translation], Moscow (1961).Google Scholar
  4. 4.
    V. M. Tikhomirov,Seme Questions of Approximation Theory [in Russian], Moscow (1976).Google Scholar
  5. 5.
    S. Fisher and C. Micchell, “Then-widths of sets of analytic functions,”Duke Math. J.,47, 789–801 (1980).MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • O. G. Parfenov

There are no affiliations available

Personalised recommendations