Asymptotic Bernstein inequality on lemniscates |
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Authors: | Béla Nagy |
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Institution: | Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary |
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Abstract: | In this paper we examine the Bernstein-Markov inequality on special compact subsets of the complex plane, namely on lemniscates. Sharp constants are obtained which involve the Green function of the complement and the density of equilibrium measure of the compact set. Using lemniscates is a useful tool because of the possibility of taking inverse images. The proof also uses so-called peaking polynomials which will be constructed. |
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Keywords: | Polynomials Markov-Bernstein inequality Green function Equilibrium measure Lemniscate Inverse image Peaking polynomials |
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