Mathematics Seminar

Let µ be a probability measure in the complex plane such that µ is supported on a union of finitely many disjoint C2+ Jordan arcs and curves γ and f be the Radon Nikodym derivative of µ with respect to the arc measure on γ. If log f ∈ L1(µγ) (this is called the Szeg condition) then the orthogonal polynomials associated with obey certain asymptotic properties (Widom 1969). Here µγ is the potential theoretic equilibrium measure of γ.

We discuss how to extend the Szego˝ condition on arbitrary non-polar compact subsets of the plane.