Undergraduate Seminar: "The Bergman space on the disc and Toeplitz operators"

Abstract: The Bergman space is a fundamental and well-studied space of analytic functions on the unit disc. Toeplitz operators are a rich class of operators or linear transformations that act on functions in the Bergman space as compressions of multiplication operators. In particular, the function-theoretic properties of the so-called symbol of the Toeplitz operator dictate its operator-theoretic properties. The Hardy space on the disc and Toeplitz operators acting on the Hardy space are perhaps more familiar objects of study, but the Bergman theory is equally interesting. In this talk, we will use ideas from operator theory, function theory, and real and complex analysis to study the Bergman space on the disc and the theory of Toeplitz operators, including Schatten class membership, boundedness, and compactness. This talk is a preview for a directed reading course led by Nathan Wagner. For instructions on how to sign up for the directed reading program, please email adeli.hutton@wustl.edu.

Host: Adeli Hutton