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
Full-text PDF Free Access
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.
- 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
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.
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.
Retrieve articles in Transactions of the American Mathematical Society with MSC: 30A82
Retrieve articles in all journals with MSC: 30A82