Derivatives of Faber Polynomials and Markov Inequalities |
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Authors: | Igor E. Pritsker |
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Affiliation: | Department of Mathematics, 401 Mathematical Sciences, Oklahoma State University, Stillwater, Oklahoma, 74078-1058, f1 |
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Abstract: | We study asymptotic behavior of the derivatives of Faber polynomials on a set with corners at the boundary. Our results have applications to the questions of sharpness of Markov inequalities for such sets. In particular, the found asymptotics are related to a general Markov-type inequality of Pommerenke and the associated conjecture of Erds. We also prove a new bound for Faber polynomials on piecewise smooth domains. |
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Keywords: | Faber polynomials derivatives asymptotics Markov inequalities. |
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