Mathematical Physics and Harmonic Analysis Seminar

Date: November 17, 2017

Time: 3:00PM - 3:50PM

Location: BLOC 220

Speaker: Maxim Zinchenko, University of New Mexico

Title: Chebyshev Polynomials on Subsets of the Real Line

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 Szego-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.

Based on Asymptotics of Chebyshev Polynomials, I. Subsets of R with J. Christiansen and B. Simon. Invent. Math. 208 (2017), 217-245, and Asymptotics of Chebyshev Polynomials, II. DCT Subsets of R with J. Christiansen, B. Simon, and P. Yuditskii (preprint arXiv:1709.06707).