Approximation Theory and its Applications

, Volume 12, Issue 1, pp 31–41 | Cite as

A property of Hermite-Padé interpolation on the roots of unity

  • T. N. T. Goodman
  • A. Sharma


We extend a theorem of Ivanov and Saff to show that for the Hermite-Padé interpolant at the roots of unity to a function meromorphic in the unit disc, its leading coefficients vanish if and only if the corresponding interpolant to a related function vanishes at given points outside the unit disc. The result is then extended to simultaneous Hermite-Padé inter polation to a finite set of functions.


Positive Integer Unit Disc Meromorphic Function Distinct Point Approximation Theory 
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Copyright information

© Springer 1996

Authors and Affiliations

  • T. N. T. Goodman
    • 1
  • A. Sharma
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of DundeeDundeeScotland, U. K.
  2. 2.Department of MathematicsUniversity of AlbertaEdmontonCanada

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