## Selected topics in Analysis: Hankel Operators and Their Applications,

Sommersemester 2015

### Location and date:

Thursdays, 9:45-11:15,

Seminarraum 8, OMP 1, 2nd Floor,

Start: 05.03.2015

End: 26.06.2015

NOTE: No lectures on 26.03 and 28.05

### Description:

The course is devoted to the theory of Hankel operators and its applications. The first part of the course can be seen as an introduction to the subject and its connections with the functions theory (Hardy spaces etc.). The second part will be devoted to the spectral theory of self-adjoint Hankel operators.

### Literature:

My lecture notes

Hankel Operators:

- 1. V. V. Peller,
*Hankel Operators and Their Applications*, Springer, New York, 2003.
- 2. N. K. Nikolski,
*Operators, Functions, and Systems: An Easy Reading, Vol. 1*, Amer. Math. Soc., Providence, 2002.
- 3. S. R. Power,
*Hankel Operators on Hilbert Space*, Pitnam, Boston, 1982.

Function Theory on the Unit Circle:

- 1. K. Hoffman,
*Banach Spaces of Analytic Functions*, Prenticee-Hall, 1962.
- 2. J. B. Garnett,
*Bounded Analytic Functions*, Academic Press, New York, 1981.
- 3. I. Katznelson,
*An Introduction to Harmonic Analysis*, Dover, New York, 1976.
- 4. C. Muscalu and W. Schlag,
*Classical and Multilinear Harmonic Analysis, Vol. 1*, Cambridge Univ. Press, 2013.