Olof Rubin
Title: Chebyshev polynomials on equipotential curves
Abstract:
Given a compact set $K\subset \mathbb C$, a Chebyshev polynomial is a monic polynomial that minimizes the supremum norm on $K$. When $K$ is infinite such a polynomial exists uniquely for each degree. Although there are no explicit formulas for computing Chebyshev polynomials, they can be studied through families of near-minimal polynomials. One such family is that of Faber polynomials, which arise naturally from the conformal map of the complement of $K$ onto the exterior of the unit disk. In this talk, I will present recent results establishing connections between Chebyshev and Faber polynomials on equipotential curves.