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Mathematical Physics Seminar

Wednesday, June 1, 2016
2:30pm to 3:30pm
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Chebyshev and orthogonal polynomials on dynamically defined Cantor sets
Maxim Zinchenko, Associate Professor, Mathematics, Universty of New Mexico,
Abstract: In this talk I'll survey recent results on the asymptotics of Chebyshev and orthogonal polynomials associated with a class of generalized Julia sets on the real line. The Chebyshev polynomials are defined as monic polynomials minimizing the sup norm over a given set. Similarly, the orthogonal polynomials are minimizers of the $L^2$ norm. We will consider polynomials orthogonal with respect to the equilibrium measure of a given set. The main results concern with the asymptotics of the corresponding norms as the degree of the polynomials tends to infinity.
 
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