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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Hermite-Birkhoff interpolation in the $n$th roots of unity
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by A. S. Cavaretta, A. Sharma and R. S. Varga PDF
Trans. Amer. Math. Soc. 259 (1980), 621-628 Request permission


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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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 259 (1980), 621-628
  • MSC: Primary 30E05
  • DOI:
  • MathSciNet review: 567101