Rice University

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Colloquium

Mathematics

Speaker: Maxim Zinchenko
University of New Mexico

Colloquium: Chebyshev Polynomials on Subsets of the Real Line

Thursday, February 16, 2017
4:00 PM  to 5:00 PM

227  Herman Brown Hall
Rice University
6100 Main St
Houston, Texas, USA

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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