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Hermite-Birkhoff interpolation in the $ n$th roots of unity

Authors: A. S. Cavaretta, A. Sharma and R. S. Varga
Journal: Trans. Amer. Math. Soc. 259 (1980), 621-628
MSC: Primary 30E05
MathSciNet review: 567101
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Abstract: Consider, as nodes for polynomial interpolation, the nth roots of unity. For a sufficiently smooth function $ f(z)$, we require a polynomial $ p(z)$ to interpolate f and certain of its derivatives at each node. It is shown that the so-called Pólya conditions, which are necessary for unique interpolation, are in this setting also sufficient.

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Keywords: Lacunary interpolation, the roots of unity, Pólya condition, Hermite-Birkhoff interpolation
Article copyright: © Copyright 1980 American Mathematical Society