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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Bernstein-type inequalities for the derivatives of constrained polynomials
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by Tamás Erdélyi PDF
Proc. Amer. Math. Soc. 112 (1991), 829-838 Request permission

Abstract:

Generalizing a number of earlier results, P. Borwein established a sharp Markov-type inequality on $[ - 1,1]$ for the derivatives of polynomials $p \in {\pi _n}$ having at most $k(0 \leq k \leq n)$ 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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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 112 (1991), 829-838
  • MSC: Primary 41A17
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1036985-7
  • MathSciNet review: 1036985