Functional and Numerical Analysis (FOMICS block course)

COURSE OBJECTIVES
Obtain knowledge on: central concepts and ideas of linear functional analysis; Banach spaces, bounded operators; compact operators; duality and representation; spectral theory

COURSE DESCRIPTION
This course provides a concise introduction to some prominent subjects in functional analysis. Starting from Banach spaces and basic topological considerations, we will consider linear and bounded operators, compact operators, and dual spaces, as well as some classical fixed-point results. We then will introduce Hilbert spaces, scalar products, and the Lax-Milgram theorem. Eventually, we will present some results from spectral theory.

LEARNING METHODS
Lecture, reading, self study, discussion, tutorial, written assignments

EXAMINATION INFORMATION
Graded assignments

REFERENCES

• Lang: Real and Functional Analysis, Springer 1993
• Brezis: Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer 2010
• Bogachev, Smolyanov: Real and Functional Analysis, Springer 2020