Markov's inequality for polynomials with real zeros

Author:
Peter Borwein

Journal:
Proc. Amer. Math. Soc. **93** (1985), 43-47

MSC:
Primary 41A17

DOI:
https://doi.org/10.1090/S0002-9939-1985-0766524-4

MathSciNet review:
766524

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Abstract: Markov's inequality asserts that for any polynomial of degree . (We denote the supremum norm on by .) In the case that has all real roots, none of which lie in , Erdös has shown that . We show that if has real roots, none of which lie in , then , where is independent of and . This extension of Markov's and Erdös' inequalities was conjectured by Szabados.

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DOI:
https://doi.org/10.1090/S0002-9939-1985-0766524-4

Article copyright:
© Copyright 1985
American Mathematical Society