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Bernstein-Type Inequalities with Bombieri Norm

Published online by Cambridge University Press:  20 November 2018

Franck Beaucoup  and
Catherine Souchon
Franck Beaucoup
Affiliation:
Ecole des Mines de Saint-Etienne, Equipe Mathématiques Appliquées, 158 cours Fauriel, 42023 Saint-Etienne, France, e-mail:beaucoup@emse.fr
Catherine Souchon
Affiliation:
Université Lyon 1, Département de Mathématiques, 69622 Villeurbanne, France, e-mail:souchon@jonas.univ-lyonl.fr
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Abstract

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If is an univariate polynomial with degree n then Bombieri norm of P is defined by

where denotes the binomial coefficient.

In the present paper we give, under assumptions on the roots of P, optimal Bernsteintype inequalities for the ratio between Bombieri norm of P and that of its derivative P′.

We also give such inequalities for the polar derivatives of P defined by

Keywords

30C1541A17polynomialBernstein inequalityBombieri normrootspolar derivatives
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 2 , 01 June 1996 , pp. 151 - 163
Copyright
Copyright © Canadian Mathematical Society 1996

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