Mathematical Physics and Harmonic Analysis Seminar

Date: April 16, 2018

Time: 1:50PM - 2:50PM

Location: BLOC 220

Speaker: Barry Simon , Caltech

Title: Szegő–Widom asymptotics for Chebyshev polynomials on subsets of R

Abstract: Chebyshev polynomials for a compact subset e ⊂ R are defined to be the monic polynomials with minimal $||·||_∞ $ over e. In 1969, Widom made a conjecture about the asymptotics of these polynomials when e was a finite gap set. We prove this conjecture and extend it also to those infinite gap sets which obey a Parreau–Widom and a Direct Cauchy Theory condition. This talk will begin with a generalities about Chebyshev Polynomials. This is joint work with Jacob Christiansen and Maxim Zinchenko and partly with Peter Yuditskii.