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Seminar on Complex Analysis (Gonchar Seminar)
May 27, 2013 18:00, Moscow, Steklov Mathematical Institute, Room 411 (8 Gubkina)
 


A Markov-type inequality and a lower bound for the moduli of critical values of polynomials

V. N. Dubinin

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok

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Abstract: A new version of the Markov-type inequality for the arbitrary plane compact sets is suggested. This inequality arises from a new distortion theorem for the complex polynomials with the constraints on their critical values. Another corollary of this theorem is an exact lower bound for maximal moduli of critical values of polynomials $P$ of degree $n$ normalized by $P(0)=0$.

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