Prof. Dr. Robert Denk
- Time: Di 10-12 in M 629, Fr 10-12 in R 513
- Exercise homepage (Tobias Nau)
Content:
This lecture gives an introduction into fundamental questions and methods of functional analysis. It is suited for students with interest in applied analysis (both from mathematics and from mathematical finance, but also for physicist).
Main topics of functional analysis are vector spaces with infinite dimension and linear mappings between them (linear operators). The related theorems analyse the underlying structures and give deeper insight in the spaces as well as in the operators. The results are important for many areas of mathematics and physics, for instance for the theory of partial differential equations, mathematical physics and numerical mathematics.
Topics of the lectures are, among others, normed spaces and Hilbert spaces, dual spaces, Hahn-Banach theorems, uniform boundedness principle and bounded and unbounded operators and their spectral decomposition.
The lecture is adapted for students in the 4th semester or higher.
Literature will be announced in the lecture.
Related modules:
This lecture course consists either of the whole semester (4+2 hours, 9 Credits) or of the first half of the semester (2+1 hours, 5 Credits). The first half of the semester is useful in particular for the students of Mathematical Finance. Here are the related modules:
Functional Analysis (4+2 hours, 9 Credits):
- Ergänzungsmodul für Bachelor Mathematik
- Wahlmodul für Master Mathematik
- Hauptstudium Diplom Mathematik
- Hauptstudium Lehramt Mathematik
Elements of Functional Analysis (=first half of the semester, 2+1 hours, 5 Credits):
- Teil des MFÖ-BA-Moduls 3: Aufbaumoduls Analysis (5 Credits, erste Hälfte der Vorlesung)
- Ergänzungsmodul für Bachelor Mathematik
- Wahlmodul für Master Mathematik
- Teil der Analysis III bzw. IV für Lehramt Mathematik
Exams:
- to be announced -