Some examples in approximation on the unit disk by reciprocals of polynomials

  • A. L. Levin
  • E. B. Saff
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1287)


This paper is a continuation of the authors’ study of approximation by reciprocals of polynomials. A Jackson-type theorem for such approximants is established for a certain class of functions f analytic and nonzero in the disk |z|<1 and continuous on |z|≤1. Furthermore, we obtain the sharp degree of convergence for reciprocal polynomial approximation on |z|≤1 to functions f that are analytic on |z|≤1, nonzero in |z|<1, and vanish somewhere on |z|=1.

AMS subject classification 41A20



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  1. 1.
    Levin A.L. and Saff E.B., Degree of approximation of real functions by reciprocals of real and complex polynomials, SIAM J. Math. Analysis (to appear).Google Scholar
  2. 2.
    Levin A.L. and Saff E.B., Jackson type theorems in approximation by reciprocals of polynomials, Rocky Mountain Journal of Mathematics (to appear).Google Scholar
  3. 3.
    Lorentz G.G., Approximation of functions, Holt, Rinehart and Winston, New York, 1966.zbMATHGoogle Scholar
  4. 4.
    Walsh J.L., On approximation to an analytic function by rational functions of best approximation, Math. Z., 38(1934), 163–176.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • A. L. Levin
    • 1
  • E. B. Saff
    • 2
  1. 1.Department of MathematicsEveryman’s UniversityTel-AvivIsrael
  2. 2.Institute for Constructive Mathematics Department of MathematicsUniversity of South FloridaTampa

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