Main content

German original

Spectral and Scattering Theory
(dt. Spektral- und Streutheorie)

Level, degree of commitment in original study programme Advanced module, compulsory elective module
Forms of teaching and learning,
workload
Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements
9 CP
Translation missing. German original:
Studienleistung: Erreichen von mindestens 50 Prozent der Punkte aus den wöchentlich zu bearbeitenden Übungsaufgaben.
Prüfungsleistung: Klausur oder mündliche Prüfung
Language,
Grading
German,
The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Mathematics.
Original study programme M.Sc. Mathematik / Vertiefungsbereich Mathematik
Duration,
frequency
One semester,
irregular
Person in charge of the module's outline Prof. Dr. Pablo Ramacher

Contents

Subject of this lecture are the spectral theory of bounded and unbounded operators on Hilbert spaces, as well as elements of scattering theory. Specifically, the following contents will be discussed:

  • The functional calculus for bounded and unbounded operators (elementary theory of C^* algebras, Gelfand-Naimark duality)
  • The Spectral Theorem for bounded and unbounded Operators
  • Existence and completeness of wave operators for trace class perturbations and the invariance principle (theorem of Kato-Rosenblum)

Qualification Goals

The students shall

  • learn to recognize and assess the relevance of spectral analytical methods for concrete problems, e.g. from the theory of partial differential equations, and to acquire the appropriate instruments for solving these problems,
  • learn how methods of algebra, analysis, geometry and topology interact,
  • Re-evaluate contents from the basic modules and some advanced modules (e.g. function theory, Analysis III and functional analysis),
  • to understand the relations of spectral theory to other fields of mathematics and other sciences,
  • practice mathematical working methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof techniques),
  • improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.

Prerequisites

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die in den Basismodulen vermittelt werden.


Recommended Reading

(not specified)



Please note:

This page describes a module according to the latest valid module guide in Wintersemester 2018/19. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.