Bernsteintype inequalities for the derivatives of constrained polynomials
Author:
Tamás Erdélyi
Journal:
Proc. Amer. Math. Soc. 112 (1991), 829838
MSC:
Primary 41A17
MathSciNet review:
1036985
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Abstract: Generalizing a number of earlier results, P. Borwein established a sharp Markovtype inequality on for the derivatives of polynomials having at most zeros in the complex unit disk. Using Lorentz representation and a Markovtype 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 Bernsteintype analogue of Borwein's Theorem. By the same method we prove a sharp Bernsteintype inequality for another wide family of classes of constrained polynomials.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199110369857
PII:
S 00029939(1991)10369857
Keywords:
Markov and Bernstein type inequalities,
polynomials with restricted zeros
Article copyright:
© Copyright 1991
American Mathematical Society
