Higher Markov and Bernstein inequalities and fast decreasing polynomials with prescribed zeros

Higher order Bernstein- and Markov-type inequalities are established for trigonometric polynomials on compact subsets of the real line and for algebraic polynomials on compact subsets of the unit circle. In the case of Markov-type inequalities we assume that the compact set satisfies an interval con...

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Bibliographic Details
Published in:Journal of approximation theory 2018-02, Vol.226, p.34-59
Main Authors: Kalmykov, Sergei, Nagy, Béla
Format: Article
Language:English
Subjects:
Algebraic polynomials
Bernstein- and Markov-type inequalities
Equilibrium measure
Fast decreasing polynomials
Green’s function
Trigonometric polynomials
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Summary:Higher order Bernstein- and Markov-type inequalities are established for trigonometric polynomials on compact subsets of the real line and for algebraic polynomials on compact subsets of the unit circle. In the case of Markov-type inequalities we assume that the compact set satisfies an interval condition.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2017.11.006