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Hardy Spaces
Dates and times
Lecture
Monday, 14:15-15:45, SR 6, Building E 2 4
Tutorial
Friday, 14:15-15:45 (every other week), SR 8, Building E 2 4
The first tutorial takes place on November 18.
Contents
Hardy spaces are Banach spaces of holomorphic functions on the unit disc in the complex plane. This topic sits at the interface of complex analysis and functional analysis. On the one hand, Hardy spaces make it possible to study holomorphic functions using tools from functional analysis. On the other hand, they provide a function theoretic approach to questions about operators on Hilbert space. A famous example is Beurling’s theorem, which completely describes all invariant subspaces of the unilateral shift. This course provides an introduction to the theory of Hardy spaces. In particular, the following topics will be covered:
- holomorphic functions on the disc and H^p spaces
- Fourier series
- factorization of H^p functions
- the unilateral shift and Beurling's theorem
Prerequisites
Complex analysis (e.g. Funktionentheorie 1) and Lebesgue integration (e.g. Analysis 3). Prior knowledge of functional analysis is helpful, but not required. In particular, this course is suitable for students who are concurrently enrolled in functional analysis.