Functional Analysis (4V, 2Ü) Prof. Wachsmuth, Dr Mehlitz
Attention
Please register for this module via Moodle before the start of the semester. Due to the current infection situation, the courses may be held in digital form.
Contents
This course teaches the basics of (linear) functional analysis. In particular, we will cover 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; Further information and working materials for the module will be provided via Moodle.
Prior knowledge
Basic knowledge of analysis, linear algebra and measure theory (as covered in the stochastics lecture).
Exercises
In the course of the semester, we will provide you with exercise sheets for the course here.
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