Fundamental constants for rational functions
S. J. Poreda, E. B. Saff and G. S. Shapiro
Trans. Amer. Math. Soc. 189 (1974), 351-358
Full-text PDF Free Access
Similar Articles |
Abstract: Suppose R is a rational function with n poles all of which lie inside , a closed Jordan curve. Lower bounds for the uniform norm of the difference on , where p is any polynomial, are obtained (in terms of the norm of R on ). In some cases these bounds are independent of as well as R and p. Some related results are also given.
J. Poreda and G.
S. Shapiro, Lower bounds for polynomial approximations to rational
functions, Proceedings of the International Conference on Padé
Approximants, Continued Fractions and Related Topics (Univ. Colorado,
Boulder, Colo., 1972; dedicated to the memory of H. S. Wall), 1974,
pp. 377–378. MR 0361095
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.
Zygmund, Trigonometrical series, Chelsea Publishing Co., New
York, 1952. 2nd ed. MR 0076084
- S. J. Poreda and G. S. Shapiro, Lower bounds for polynomial approximations to rational functions, Rocky Mountain J. Math. (to appear). MR 0361095 (50:13541)
- 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.
- A. Zygmund, Trigonometrical series, 2nd ed. reprinted with corrections and some additions, Cambridge Univ. Press, New York, 1968. MR 38 #4882. MR 0076084 (17:844d)
Retrieve articles in Transactions of the American Mathematical Society
Retrieve articles in all journals
closed Jordan curve
© Copyright 1974
American Mathematical Society