Extremal Problems in Spaces of Analytic Functions
Document Type
Lecture
Publication Date
2-26-2014
Abstract
Extremal problems have long played an important role in complex analysis. For example, the proof of the Riemann mapping theorem involves an extremal problem, and the famous Bieberbach conjecture (proved by de Branges) is about an extremal problem. I will discuss some of my recent results about extremal problems in spaces of analytic functions, particularly Bergman spaces and Fock spaces. The results will include regularity properties and some explicit solutions. I will also talk about a surprising connection between an extremal problem involving Toeplitz operators, the first eigenvalue of the Laplacian, and related quantity called the torsional rigidity.
Relational Format
presentation
Recommended Citation
Ferguson, Timothy, "Extremal Problems in Spaces of Analytic Functions" (2014). Colloquium. 25.
https://egrove.olemiss.edu/math_colloquium/25
