Szego Seminar: "Natural Boundaries in Function Theory"

Alberto Dayan, Washington University in Saint Louis

Abstract: The aim of this talk is to give some conditions on the coefficients of a complex valued power series so that the circle of convergence of the power series is its natural boundary. Namely, every point on the circle of convergence is a singularity of the power series. After a review of well known results due to Fabry, Pólya and Szegö, we will examine the probabilistic case by defining a random power series and looking for conditions on the random coefficients that imply a natural boundary almost surely. 

 

Host: Christopher Felder