Complex Analysis and Operator Theory

, Volume 6, Issue 3, pp 651–664 | Cite as

An Extension of Fejér’s Condition for Hermite Interpolation

  • Elías Berriochoa
  • Alicia Cachafeiro
  • José M. García-Amor
Article

Abstract

We study the Hermite interpolation problem with equally spaced nodes on the unit circle. We obtain new conditions for the derivatives in order that the Hermite interpolants uniformly converge to continuous functions. As a consequence we obtain some improvements in the case of the bounded interval.

Keywords

Hermite interpolation Hermite-Fejér interpolation Laurent polynomials Convergence Unit circle Fejér’s condition Conjugate exponents 

Mathematics Subject Classification (2000)

Primary 65D05 Secondary 41A05 42A15 33C45 26D20 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Elías Berriochoa
    • 1
  • Alicia Cachafeiro
    • 2
  • José M. García-Amor
    • 2
  1. 1.Departamento de Matemática Aplicada IFacultad de Ciencias Universidad de VigoOurenseSpain
  2. 2.Departamento de Matemática Aplicada IE.T.S. Ingenieros Industriales Universidad de VigoVigoSpain

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