Fundamental constants for rational functions
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- by S. J. Poreda, E. B. Saff and G. S. Shapiro PDF
- Trans. Amer. Math. Soc. 189 (1974), 351-358 Request permission
Abstract:
Suppose R is a rational function with n poles all of which lie inside $\Gamma$, a closed Jordan curve. Lower bounds for the uniform norm of the difference $R - p$ on $\Gamma$, where p is any polynomial, are obtained (in terms of the norm of R on $\Gamma$). In some cases these bounds are independent of $\Gamma$ as well as R and p. Some related results are also given.References
- S. J. Poreda and G. S. Shapiro, Lower bounds for polynomial approximations to rational functions, Rocky Mountain J. Math. 4 (1974), 377–378. MR 361095, DOI 10.1216/RMJ-1974-4-2-377 A. I. Markuševič, Theory of analytic functions, GITTL, Moscow, 1950; English transl., Theory of functions of a complex variable, Prentice-Hall, Englewood Cliffs, N. J., 1967. MR 12,87; MR 35 #6799.
- Antoni Zygmund, Trigonometrical series, Chelsea Publishing Co., New York, 1952. 2nd ed. MR 0076084
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 189 (1974), 351-358
- MSC: Primary 30A82
- DOI: https://doi.org/10.1090/S0002-9947-1974-0361096-8
- MathSciNet review: 0361096