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Operator Theory

Module MA5012

This Module is offered by Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of WS 2011/2 (current)

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2011/2SS 2011

Basic Information

MA5012 is a semester module in English language at Master’s level which is offered once.

This Module is included in the following catalogues within the study programs in physics.

  • Focus Area Theoretical Quantum Science & Technology in M.Sc. Quantum Science & Technology
  • Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)
Total workloadContact hoursCredits (ECTS)
270 h 90 h 9 CP

Content, Learning Outcome and Preconditions


Spectrum of operators, spectral theory of normal operators, functional calculus for various classes of operators. Applications for integral operators and differential operators.

Learning Outcome

At the end of module, students are able to analyze and synthesize various operators showing up when dealing with partial differential equations and inverse problems.


MA3001 Functional Analysis

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 4 Operator Theory Warzel, S.

Learning and Teaching Methods

The module is offered as lectures with accompanying practice sessions.
In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should encourage the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding the lectures, practice sessions will be offered, in which students will be working through exercises provided in class. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress. As the term progresses, students will be working increasingly independently or in small groups towards their course project.




Dunford, Schwartz: Linear Operators I-III, Wiley-Interscience 1988.
Weidmann: Lineare Operatoren im Hilbertraum, Teubner 1986.
Werner: Funktionalanalysis, Springer 2007.

Module Exam

Description of exams and course work

The module examination is based on a written exam (90 minutes). Students have to understand the fundamental notions, techniques and methods in spectral theory and be able to apply them to simple examples.

Exam Repetition

The exam may be repeated at the end of the semester.

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