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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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A characterization of badly approximable functions
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by S. J. Poreda PDF
Trans. Amer. Math. Soc. 169 (1972), 249-256 Request permission

Abstract:

Complex valued functions, continuous on a closed Jordan curve in the plane and having the property that all of their polynomials of best uniform approximation on that curve are identically zero are characterized in terms of their mapping properties on that curve.
References
  • A. I. Markushevich, Theory of functions of a complex variable. Vol. III, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. Revised English edition, translated and edited by Richard A. Silverman. MR 0215964
  • J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XX, American Mathematical Society, Providence, R.I., 1960. MR 0218587
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 169 (1972), 249-256
  • MSC: Primary 30A82
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0306510-7
  • MathSciNet review: 0306510