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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. Markuševič, Theory of functions of a complex variable. Vol. III, GITTL, Moscow, 1950; English transl., Prentice-Hall, Englewood Cliffs, N. J., 1967. MR 12, 87; MR 35 #6799. MR 0215964 (35:6799)
  • [2] J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, 3rd ed., Amer. Math. Soc. Colloq. Publ., vol. 20, Amer. Math. Soc., Providence, R. I., 1960. MR 36 #1672a. MR 0218587 (36:1672a)

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Keywords: Badly approximable functions, best uniform approximation, closed Jordan curve
Article copyright: © Copyright 1972 American Mathematical Society

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