312.103 (17W) Funktionalanalysis
Überblick
- Lehrende/r
- LV-Titel englisch Functional Analysis
- LV-Art Vorlesung-Übung (prüfungsimmanente LV )
- Semesterstunde/n 2.0
- ECTS-Anrechnungspunkte 3.0
- Anmeldungen 11 (25 max.)
- Organisationseinheit
- Unterrichtssprache es wurde keine Unterrichtssprache angegeben
- LV-Beginn 03.10.2017
Zeit und Ort
LV-Beschreibung
Intendierte Lernergebnisse
Understanding of strongly continuous semigroups.
Lehrmethodik inkl. Einsatz von eLearning-Tools
Lecture
Inhalt/e
Initial point of the course is Cauchy’s functional equation, i.e. the problem to classify those functions T(t), which satisfy the semigroup property
T(t+s)=T(t)T(s) for all nonnegative t,s
This seemingly theoretical question has not only far reaching applications in ordinary, partial and functional differential equations, but also requires to develop an interesting functional analytical machinery. Among these tools are closed operators and their spectrum (which extends the rather trivial results from Linear Algebra), the important special case of compact operators, linear semigroups and their generators. Moreover, we provide a modern application to time-dependent ordinary differential equations in terms of evolution families.
Contents
- Spectral theory for closed operators
- Riesz-Schauder theory for the spectrum of compact operators
- Linear semigroups and their generators
- Hille-Yosida theorem characterising the solutions to Cauchy’s equation
- Evolution families
Erwartete Vorkenntnisse
Analysis, Linear Algebra, Ordinary differential equations, Basics on Functional Analysis, some knowledge on evolutionary PDEs won't hurt
Literatur
K.J. Engel & R. Nagel: One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics 194, Springer, Berlin, 2000
A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, Springer, Berlin, 1983
K. Yosida: Functional Analysis, Grundlehren der Mathematischen Wissenschaften 123, Springer, Berlin, 1980
Prüfungsinformationen
Prüfungsmethode/n
oral examination (45 min) after the last lecture, by appointment
Prüfungsinhalt/e
contents of the course
Beurteilungskriterien/-maßstäbe
familiarity with the contents of the course
Beurteilungsschema
Note BenotungsschemaPosition im Curriculum
- Doktoratsprogramm Modeling-Analysis-Optimization of discrete, continuous and stochastic systems
(SKZ: ---, Version: 16W.1)
-
Fach: Modeling-Analysis-Optimization of discrete, continuous and stochastic systems
(Pflichtfach)
-
Modeling-Analysis - Optimization of discrete, continuous and stochastic systems (
0.0h XX / 0.0 ECTS)
- 312.103 Funktionalanalysis (2.0h VU / 3.0 ECTS)
-
Modeling-Analysis - Optimization of discrete, continuous and stochastic systems (
0.0h XX / 0.0 ECTS)
-
Fach: Modeling-Analysis-Optimization of discrete, continuous and stochastic systems
(Pflichtfach)
- Masterstudium Technische Mathematik
(SKZ: 401, Version: 13W.1)
-
Fach: Analysis
(Pflichtfach)
-
Funktionalanalysis (
2.0h VU / 3.0 ECTS)
- 312.103 Funktionalanalysis (2.0h VU / 3.0 ECTS)
-
Funktionalanalysis (
2.0h VU / 3.0 ECTS)
-
Fach: Analysis
(Pflichtfach)