Current situation

Due to the current situation in Germany and the world, it can be assumed that the seminar will be held online. Therefore, we would like to ask you to contact Prof. Wachsmuth as soon as possible if you are interested in the seminar so that we can coordinate the further procedure.

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).

Exercises

Examination

In order to take a module examination, an oral examination takes place after the lecture period. The list of possible exam questions can be helpful in preparing for the exam.

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