Sommersemester 2020

Functionalanalysis 2

Dr. Elke Rosenberger

This lecture is the continuation of the lecture Functional Analysis 1.

Bitte melden Sie sich auch bei dem moodle-Kurs Funktionalanalysis 2 an. Dort werden die entsprechenden Informationen zur Durchführung des Kurses stehen, solange noch keine Präsenzveranstaltungen durchgeführt werden können.

Please also register at the course Functional analysis 2 on moodle. There all informations concerning the realization of the course will be available while it is not possible to give a presence lecture, i.e. to actually be present at the university.

Ü   Mo   12:15 - 13:45 Uhr;  
V   Di     10:15 - 11:45 Uhr;  
V   Do    14:15 - 15:45 Uhr;

Literatur: 

- Michael Reed, Barry Simon: Methods of Modern Mathematical Physics 1 - 2
- Dirk Werner: Funktionalanalysis
- Walter Rudin: Functional Analysis

Lerninhalte:

In the beginning, different versions of the Spectral Theorem for bounded self-adjoint operators are presented. Then the theory of unbounded self-adjoint operators is introduced, including the Spectral Theorem, Stones Theorem, Friedrichs Extension, Von Neumanns Theorem, Trotter-Kato Theorem and the Trotter Product Formula. After a short repetition of Fourier transformations und distributions, Sobolev spaces are defined and the Sobolev Lemma is given. Then some examples for self-adjoint operators are discussed.

Seminar:  Semiclassical and Microlocal Analysis

Dr. Elke Rosenberger

We will read and discuss the book "An Introduction to Semiclassical and Microlocal Analysis" written by Andre Martinez.

S   Di    16:15 - 17:45 Uhr

Literatur:

 - Andre Martinez: An Introduction to Semiclassical and Microlocal Analysis

Lerninhalte:

Symbol spaces and Semiclassical Pseudofifferential Operators, Quantization, Microlocalization, Characteristic set