A property of Hermite-Padé interpolation on the roots of unity
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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.
KeywordsPositive Integer Unit Disc Meromorphic Function Distinct Point Approximation Theory
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- .Goodman, T. N. T., Ivanov, K. G. and Sharma, A., Hermite Interpolation in the Roots of Unity, J. Approximation Theory (to appear).Google Scholar