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Transactions of the American Mathematical Society

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A characterization of badly approximable functions


Author: S. J. Poreda
Journal: Trans. Amer. Math. Soc. 169 (1972), 249-256
MSC: Primary 30A82
MathSciNet review: 0306510
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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 [Enhancements On Off] (What's this?)

  • [1] A. I. Markushevich, Theory of functions of a complex variable. Vol. III, Revised English edition, translated and edited by Richard A. Silverman, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0215964
  • [2] J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, Third edition. American Mathematical Society Colloquium Publications, Vol. XX, American Mathematical Society, Providence, R.I., 1960. MR 0218587

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0306510-7
Keywords: Badly approximable functions, best uniform approximation, closed Jordan curve
Article copyright: © Copyright 1972 American Mathematical Society