Bernstein- and Markov-type inequalities for rational functions

2016/10/21 by Kalmykov, Sergei, Nagy, Béla, Totik, Vilmos
#30C85 #41A17 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1610.06706

Abstract

Asymptotically sharp Bernstein- and Markov-type inequalities are established for rational functions on C² smooth Jordan curves and arcs. The results are formulated in terms of the normal derivatives of certain Green's functions with poles at the poles of the rational functions in question. As a special case (when all the poles are at infinity) the corresponding results for polynomials are recaptured.

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