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This entry is from Winter semester 2022/23 and might be obsolete. You can find a current equivalent here.
Fourier Integral Operators
(dt. Fourier-Integraloperatoren)
Level, degree of commitment | Specialization 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 Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises. Examination type: Written or oral examination |
Language, Grading |
German (Standard) and English (bei Bedarf),The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics. |
Duration, frequency |
One semester, Regularly alternating with other specialization modules im Gebiet Analysis |
Person in charge of the module's outline | Prof. Dr. Pablo Ramacher |
Contents
- Oscillatory integrals
- Fourier integral operators and pseudo-differential operators in Euclidean space
- Pseudo-differential operators on manifolds and their spectral theory, Sobolev spaces
- Hamilton-Jacobi theory, symplectic geometry, Lagrangian submanifolds
- Global theory of Fourier integral operators on manifolds
Qualification Goals
The students shall
- to get to know and use the theory of Fourier integral operators as a central area of analysis and be introduced to questions of current research,
- Apply knowledge from functional analysis, Fourier and distribution theory to the modern theory of partial differential equations,
- 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
None. The competences taught in the following modules are recommended: either Analysis I and Analysis II or Basic Real Analysis, Complex Analysis and Vector Analysis, Functional Analysis, Partial Differential Equations.
Applicability
Module imported from M.Sc. Mathematics.
It can be attended at FB12 in study program(s)
- B.Sc. Mathematics
- M.Sc. Mathematics
- M.Sc. Business Mathematics
When studying M.Sc. Business Mathematics, this module can be attended in the study area Specialization and Practical Modules in Mathematics.
The module is assigned to Pure Mathematics. Further information on eligibility can be found in the description of the study area.
Recommended Reading
- Shubin, M. A., Pseudodifferential operators and spectral theory; Grigis, A. and Sjoestrand, J., Microlocal analysis for differential operators; Duistermaat, J.J., Fourier integral operators.
Please note:
This page describes a module according to the latest valid module guide in Winter semester 2022/23. 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:
- Winter 2016/17 (no corresponding element)
- Summer 2018
- Winter 2018/19
- Winter 2019/20
- Winter 2020/21
- Summer 2021
- Winter 2021/22
- Winter 2022/23
- Winter 2023/24
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.