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Journal of Mathematical Sciences

, Volume 96, Issue 2, pp 2966–2972 | Cite as

A study of the rate of rational approximation of a class of analytic functions

  • A. Ya. Radyno
Article
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Abstract

This paper is devoted to results belonging to the theory of rational approximation of analytic functions. We study the rate of decrease of the best approximations ρn of a functionf holomorphic in a disk ¦z ∶ ¦z¦< ρ, ρ>1> by rational functions of order at most n in the uniform metric on the unit disk with center at z=0. We prove theorems that connect the rate of decrease of the quantities ρn with the order σ≥0 and type Τ≥0 of the functionf. The proofs of these results are based on the methods of the theory of Hankel operators.

Keywords

Rational Function Analytic Function Unit Disk Rational Approximation Hankel Operator 
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Literature cited

  1. 1.
    V. M. Adamyan, D. Z. Arov, and M. G. Krein,Mat. Sb.,86 (128), No. 1 (9), 34–75 (1971).Google Scholar
  2. 2.
    I. Ts. Gokhberg and M. G. Krein,Introduction to the Theory of Linear Nonselfadjoint Operators, American Mathematical Society, Providence (1969).Google Scholar
  3. 3.
    O. G. Parfenov,Mat. Sb.,131 (173), 501–518 (1986).Google Scholar
  4. 4.
    I. I. Privalov,Randeigenschaften analytischer Funktionen, Deutscher Verlag der Wissenschaften, Berlin (1956).Google Scholar
  5. 5.
    V. A. Prokhorov,Mat. Sb.,184, No. 1, 89–104 (1993).Google Scholar
  6. 6.
    V. A. Prokhorov,Mat. Sb.,184, No. 2, 3–32 (1993).Google Scholar
  7. 7.
    T. Ts. Tumarkin and S. Yu. Khavinson,Usp. Mat. Nauk,13, No. 1, 201–206 (1958).Google Scholar
  8. 8.
    K. Menke,Comp. Var. Theory Appl,2, No. 2, 165–175 (1983).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • A. Ya. Radyno

There are no affiliations available

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