Mathematical Physics Seminar

Given a compact subset, E in R, the Chebyshev polynomials are the
unique minmizers of the sup norm over E among all degree n monic
polynomials. I will describe some recent results of Christensen, Simon
and Zinchenko on this classical subject. We settle a 45 year old
conjecture of Widom on the large n pointwise asymptotics for the case
of finite gap sets. We also extend upper bounds on the norm that Totik
and Widom obtained for the finite gap case to positive measure Cantor
sets. Our proof in this case is new and even in the finite gap case is
simpler and more explicit bounds than the earlier work.