Abstract
This paper is a continuation of the authors’ study of approximation by reciprocals of polynomials. A Jackson-type theorem for such approximants is established for a certain class of functions f analytic and nonzero in the disk |z|<1 and continuous on |z|≤1. Furthermore, we obtain the sharp degree of convergence for reciprocal polynomial approximation on |z|≤1 to functions f that are analytic on |z|≤1, nonzero in |z|<1, and vanish somewhere on |z|=1.
AMS subject classification 41A20
- 41A17
The research of this author was conducted while visiting the Institute for Constructive Mathematics at the University of South Florida.
The research of this author was supported, in part, by the National Science Foundation.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Levin A.L. and Saff E.B., Degree of approximation of real functions by reciprocals of real and complex polynomials, SIAM J. Math. Analysis (to appear).
Levin A.L. and Saff E.B., Jackson type theorems in approximation by reciprocals of polynomials, Rocky Mountain Journal of Mathematics (to appear).
Lorentz G.G., Approximation of functions, Holt, Rinehart and Winston, New York, 1966.
Walsh J.L., On approximation to an analytic function by rational functions of best approximation, Math. Z., 38(1934), 163–176.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag
About this paper
Cite this paper
Levin, A.L., Saff, E.B. (1987). Some examples in approximation on the unit disk by reciprocals of polynomials. In: Saff, E.B. (eds) Approximation Theory, Tampa. Lecture Notes in Mathematics, vol 1287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078898
Download citation
DOI: https://doi.org/10.1007/BFb0078898
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18500-0
Online ISBN: 978-3-540-47991-8
eBook Packages: Springer Book Archive
