http://dx.doi.org/10.1006/jath.1997.3230

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Title

On the Bernstein inequality for rational functions with a prescribed zero

Authors

Authors

R. Jones; X. Li; R. N. Mohapatra;R. S. Rodriguez

Comments

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Abbreviated Journal Title

J. Approx. Theory

Keywords

rational functions; Bernstein inequality; Blaschke product; POLYNOMIALS; Mathematics

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 at z=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. (C) 1998 Academic Press.

Journal Title

Journal of Approximation Theory

Volume

95

Issue/Number

3

Publication Date

1-1-1998

Document Type

Article

Language

English

First Page

476

Last Page

496

WOS Identifier

WOS:000077443200005

ISSN

0021-9045

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