Functional Analysis (4V, 2Ü) Prof. Wachsmuth

Contents

This course teaches the basics of (linear) functional analysis. In particular, we will deal with the following points:

• Metric spaces
• Banach and Hilbert spaces, ^Lp-spaces, Sobolev spaces
• Linear continuous operators
• Linear functionals, dual spaces, the Hahn-Banach theorem
• Principle of uniform boundedness, closed graph theorem, continuous inverse theorem, open mapping theorem
• Fredholm theory
• Spectral theory

Associated module: 11303

Prior knowledge

Basic knowledge of analysis, linear algebra and measure theory (as covered in the stochastics lecture).

Current

• The first lecture will take place on 03.04.2018 (instead of the exercise). The first exercise is on 10/04/2018.

Examination

In order to take a module examination, an oral examination will take place after the lecture period. The list of possible exam questions may be helpful for preparation.

Supplementary literature

The following books are a good supplement to the lecture, in particular they also contain many exercises and further material. They are available free of charge as e-books at BTU Cottbus-Senftenberg (see links) and some are available in the library.

• Winfried Kaballo, Basic Course in Functional Analysis, Springer, 2018
• Hans Wilhelm Alt, Linear Functional Analysis, Springer, 2016
• Dirk Werner, Functional Analysis, Springer, 2011
• Manfred Dobrowolski, Applied Functional Analysis, Springer, 2010
• Martin Brokate and Götz Kersting, Measure and Integral, Springer, 2011