Bernstein-type inequalities for the derivatives of constrained polynomials

Author:
Tamás Erdélyi

Journal:
Proc. Amer. Math. Soc. **112** (1991), 829-838

MSC:
Primary 41A17

MathSciNet review:
1036985

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Abstract: Generalizing a number of earlier results, P. Borwein established a sharp Markov-type inequality on for the derivatives of polynomials having at most zeros in the complex unit disk. Using Lorentz representation and a Markov-type inequality for the derivative of Müntz polynomials due to D. Newman, we give a surprisingly short proof of Borwein's Theorem. The new result of this paper is to obtain a sharp Bernstein-type analogue of Borwein's Theorem. By the same method we prove a sharp Bernstein-type inequality for another wide family of classes of constrained polynomials.

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DOI:
https://doi.org/10.1090/S0002-9939-1991-1036985-7

Keywords:
Markov and Bernstein type inequalities,
polynomials with restricted zeros

Article copyright:
© Copyright 1991
American Mathematical Society