Advertisement

On equiconvergence of certain sequences of rational interpolants

  • E. B. Saff
  • A. Sharma
Convergence Theory
Part of the Lecture Notes in Mathematics book series (LNM, volume 1105)

Abstract

For a function f(z) analytic on |z| < ρ, ρ > 1, we consider two schemes of rational interpolants which have poles equally spaced on the circle |z|=σ, σ > 1. The first scheme interpolates f(z) in the roots of unity, while the second consists of best L2-approximants to f(z) on the unit circle. We obtain precise regions of equiconvergence for the two schemes of rational functions, thus extending a well-known result of J. L. Walsh.

Keywords

Rational Function Unit Circle Interpolation Property Precise Region Rational Interpolation 
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.

References

  1. 1.
    A. S. Cavaretta Jr., A. Sharma and R. S. Varga. Interpolation in the roots of unity: An extension of a theorem of J. L. Walsh. Resultate der Math. 1981, vol. 3, 155–191.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    G. López Lagomasino and René Piedra de la Torre, Sbore un teorema de sobreconvergencia de J. L. Walsh. Revista Ciencias Matemáticas. 1983, vol. IV, No. 3, 67–78.Google Scholar
  3. 3.
    E. B. Staff, A. Sharma and R. S. Varga, An extension to rational functions of a theorem of J. L. Walsh on differences of interpolating polynomials, R.A.I.R.O. Analyse numérique, 1981, vol. 15, 371–390.MathSciNetzbMATHGoogle Scholar
  4. 4.
    R. S. Varga. Topics in Polynomial and Rational Interpolation and Approximation. Séminaire de Math. Supérieures, Les Presses de L'Univ. de Montréal, Montréal, 1982, 69–93.Google Scholar
  5. 5.
    J. L. Walsh. Interpolation and Approximation by Rational Functions in the Complex Domain. A.M.S. Colloq. Publ. Vol XX, Providence, R.I., 5th ed. 1969.Google Scholar
  6. 6.
    A. Zygmund, Trigonometric Series, Vol. II, University Press, Cambridge, 2nd ed. 1959.Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • E. B. Saff
    • 1
  • A. Sharma
    • 2
  1. 1.Center for Mathematical ServicesUniversity of South FloridaTampa
  2. 2.Mathematics DepartmentUniversity of AlbertaEdmontonCanada

Personalised recommendations