## Michael Hartz

## Hardy Spaces

(Winter term 2019/2020)### News

Assignment 5 is online.### Time and Place

**Lecture (Dec 10 - Feb 7):**

Tuesday, 10:15-11:45, SR2

Thursday, 16:00-17:30, SR10

**Exercise session:**Monday, 10:15-11:45, HS4 (run by Dominik Schillo)

**Office Hour:**Tuesday, 12:00-13:00, or by appointment

### Assignments

Assignment 1, due December 19.Assignment 2, due January 9.

Assignment 3, due January 16.

Assignment 4, due January 23.

Assignment 5, due January 30.

### 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 Beurlingâ€™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:- Fourier series,
- holomorphic functions on the disc and H
^{p}spaces, - factorization of H
^{p}functions, - the disc algebra,
- the unilateral shift

### Literature

Main text:Hoffman, Kenneth,

*Banach Spaces of Analytic Functions*, 2007.

Additional literature:

Duren, Peter L,

*Theory of H*, 2003.

^{p}SpacesGarnett, John B.,

*Bounded Analytic Functions*, 2006.

Koosis, Paul,

*Introduction to H*, 1999.

^{p}SpacesNikolski, Nikolai,

*Hardy Spaces*, 2019.

Last update: November 29, 2019 Michael Hartz | Impressum |