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Hilbert Function Spaces
Dates and times
Lecture
Thursday, 14:15-15:45, HS 4, Building E 2 4
Tutorial
Monday, 10:15-11:45, SR 1, Building E 2 5
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. Concretely, you need to present at least one solution to a regular assignment problem, and also give a short presentation towards the end of the semester (list of topics will follow).