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Bernstein and Markov Type Inequalities for Generalized Non-Negative Polynomials

Published online by Cambridge University Press:  20 November 2018

Tamás Erdélyi
Tamás Erdélyi*
Affiliation:
Department of Mathematics The Ohio State University 231 West Eighteenth Avenue Columbus, Ohio 43210-1174, USA
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Abstract

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Generalized polynomials are defined as products of polynomials raised to positive real powers. The generalized degree can be introduced in a natural way. Several inequalities holding for ordinary polynomials are expected to be true for generalized polynomials, by utilizing the generalized degree in place of the ordinary one. Based on Remez-type inequalities on the size of generalized polynomials, we establish Bernstein and Markov type inequalities for generalized non-negative polynomials, obtaining the best possible result up to a multiplicative absolute constant.

Keywords

41A17Generalized PolynomialsBernstein InequalityMarkov Inequality
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 3 , 01 June 1991 , pp. 495 - 505
Copyright
Copyright © Canadian Mathematical Society 1991

References

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