Analysis and PDE seminar: Catherine Bénéteau

Speaker: Catherine A. Bénéteau, Associate Professor, Department of Mathematics and Statistics, University of South Florida.

Title: Polynomial Solutions to an Optimization Problem in Classical Analytic Function Spaces. Part III.
Abstract: In this series of talks, I will introduce some classical spaces of analytic functions in the unit disk in the complex plane called Dirichlet type spaces. Examples of these spaces include the Hardy space (functions whose coefficients are square summable), the Bergman space (functions whose modulus squared is integrable with respect to area measure over the whole disk), and the (classical) Dirichlet space (functions whose image has finite area, counting multiplicity). I will discuss polynomials that solve an optimization problem that I will describe. These polynomials are intimately connected to some classical tools in analysis: reproducing kernels and orthogonal polynomials. In particular, I will examine the clusters of the zeros of these optimal polynomials and show how their location depends on the space being considered.