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)


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.


Rational Function Unit Circle Interpolation Property Precise Region Rational Interpolation 
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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

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