Student Analysis Seminar

The study of orthogonal polynomials with respect to positive weights is a classical topic which stemmed from the study of continued fractions, and has since found use in a truly impressive list of fields of mathematics, including approximation theory, mathematical physics, and numerical analysis (to name very, very few). However, as soon as one steps into the world of complex-valued weights, many of the familiar properties and results no longer hold, and one is left to realize that the positivity of the weight played a critical role in the richness of the classical theory of orthogonal polynomials. In this talk, I will discuss the definition and some of the basic properties of classical orthogonal polynomials and their sharp contrast with the case of complex-valued weights, while highlighting one particular application: quadrature rules. Speaker(s): Ahmad Barhoumi (University of Michigan)