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Instructors: Prof. Dr. rer. nat. Dieter Bothe; Dr. rer. nat. Mathis Fricke
Event type:
Lecture & Exercise
Org-unit: Dept. 04 - Mathematics
Displayed in timetable as:
Func. Ana.
Subject:
Crediting for:
Hours per week:
6
Language of instruction:
German
Min. | Max. participants:
- | -
Course Contents:
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.
Literature:
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;
Preconditions:
recommended: Analysis, Integration Theory, Complex Analysis, Linear Algebra or comparable prerequisites acquired in mathematics courses in engineering programmes
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