### PD Dr. Erich Walter Farkas

###
Lecture in Summer Term 2004

## Spectral Theory for Unbounded Operators

**Lectures:** Wed. 14-18, room E39, **each two weeks**

Starting date: 21. April 2004.

The other lectures: 5. Mai, 19. Mai, 2. June, 16. June, 30. June.

Last lecture **Thu. 15. July, 12-14, room E40 **

**Motivation:**
This lecture can be regarded as a second part of the lecture
Functional Analysis
(from the previous semester).

Moreover, our intention is to complement with backgroud material the lecture

"Mathematical Methods in
Physics: Quantum Mechanics"

**Content:** The following topics will be covered:
- Unbounded Operators
- The energy space, Friedrichs' extension
- Spectra of self adjoint operators
- Spectral families and spectral operators
- Fundamental theorem of the spectral theory
- Operators with a pure point spectrum

If requested, an exercise session can be organized.

**Literature:** M. Reed, B. Simon: Methods of Modern Mathematical Physics, Vol I:
Functional Analysis;

Vol II:
Fourier Analysis, Self-Adjointness;
Orlando, Academic Press, 1980.

**For:** Students in the International Master Program;

Students of mathematics and physics after the fifth semester.

**Prerequisites:**
A first course in functional analysis is welcome, but not mandatory.

Introductory courses in analysis and linear algebra.

**Certificate (Schein)**: 1/2 - Gilt für Diplomhauptprüfung (AM);
Hauptprüfung für das Lehramt an Gymnasien.

** Office hours: **
PD Dr. E.W. Farkas: appointment should be arranged after the lectures

##

Please send comments and suggestions to
Walter Farkas,
email: farkas@math.ethz.ch.
Last modified: Fri Jul 2 09:29:50 CEST 2004