Title
On the Bernstein Inequality for Rational Functions with a Prescribed Zero
Keywords
Rational functions; Bernstein inequality; Blaschke product
Abstract
We extend some results of Giroux and Rahman (Trans. Amer. Math. Soc.193(1974), 67-98) for Bernstein-type inequalities on the unit circle for polynomials with a prescribed zero atz=1 to those for rational functions. These results improve the Bernstein-type inequalities for rational functions. The sharpness of these inequalities is also established. Our approach makes use of the Malmquist-Walsh system of orthogonal rational functions on the unit circle associated with the Lebesgue measure. © 1998 Academic Press.
Publication Date
12-1-1998
Publication Title
Journal of Approximation Theory
Volume
95
Issue
3
Number of Pages
476-496
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1006/jath.1997.3230
Copyright Status
Unknown
Socpus ID
0038905815 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/0038905815
STARS Citation
Jones, Roy; Li, Xin; and Mohapatra, R. N., "On the Bernstein Inequality for Rational Functions with a Prescribed Zero" (1998). Scopus Export 1990s. 3635.
https://stars.library.ucf.edu/scopus1990/3635