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

Socpus ID

0038905815 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0038905815

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