Lehrinhalte
Normed vector spaces, completion; Theorem of Hahn-Banach, Theorem of Banach-Steinhaus, Open Mapping Theorem, Closed Graph Theorem; Hilbert spaces; reflexive spaces, weak convergence; Sobolev spaces, weak solution of the Dirichlet problem; spectral properties of linear operators; compact operators on Banach spaces, spectral theorem for compact operators.
Literatur
Alt: Lineare Funktionalanalysis;
Conway: A Course in Functional Analysis;
Reed, Simon: Functional Analysis: Methods of Modern Mathematical Physics I;
Rudin: Functional Analysis;
Werner: Funktionalanalysis;
Ciarlet: Functional Analysis;
Voraussetzungen
recommended: Analysis, Integration Theory, Complex Analysis, Linear Algebra or comparable prerequisites acquired in mathematics courses in engineering programmes
Normed vector spaces, completion; Theorem of Hahn-Banach, Theorem of Banach-Steinhaus, Open Mapping Theorem, Closed Graph Theorem; Hilbert spaces; reflexive spaces, weak convergence; Sobolev spaces, weak solution of the Dirichlet problem; spectral properties of linear operators; compact operators on Banach spaces, spectral theorem for compact operators.
Literatur
Alt: Lineare Funktionalanalysis;
Conway: A Course in Functional Analysis;
Reed, Simon: Functional Analysis: Methods of Modern Mathematical Physics I;
Rudin: Functional Analysis;
Werner: Funktionalanalysis;
Ciarlet: Functional Analysis;
Voraussetzungen
recommended: Analysis, Integration Theory, Complex Analysis, Linear Algebra or comparable prerequisites acquired in mathematics courses in engineering programmes
- Lehrende: Anonym
- Lehrende: BotheDieter
Semester: WT 2019/20