Rice University Department of Mathematics Colloquium

Chebyshev Polynomials on Subsets of the Real Line

4:00 pm Thursday, February 16th, 2017
Maxim Zinchenko (University of New Mexico)

Abstract: Chebyshev polynomials are the unique monic polynomials that minimize the sup-norm on a given compact set. These polynomials have important applications in approximation theory and numerical analysis. H. Widom in his 1969 influential work initiated a study of Szeg\H{o}-type asymptotics of Chebyshev polynomials on compact sets given by finite unions of disjoint arcs in the complex plane. He obtained several partial results on the norm and pointwise asymptotics of the polynomials and made several long lasting conjectures. In this talk I will present some of the classical results on Chebyshev polynomials as well as recent progress on Widom's conjecture on the large n asymptotics of Chebyshev polynomials on finite and infinite gap subsets of the real line.

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