Hilbert Function Spaces

Hilbert Function Spaces

Dates and times

Lecture

Thursday, 14:15-15:45, HS 4, Building E 2 4

Tutorial

TBD

Contents

This course is an introduction to the theory of Hilbert function spaces. A particular focus lies on the modern theory of Pick spaces, which provides a functional analytic approach to function theoretic
questions such as interpolation and factorization of functions.

Topics covered:

• Hilbert function spaces and reproducing kernels
• multipliers
• Pick spaces and characterization theorems of McCullough-Quiggin and Agler-McCarthy
• Leech's theorem on factorization
• Beurling's theorem on invariant subspaces

Prerequisites

Functional Analysis and Complex Analysis

Exam

There will be an oral exam at the end of the semester. In order to be eligible for the exam, you have to actively participate in the tutorials and present some of your solutions to assignment problems.

Literature

TBA