250384 VO Selected topics in applied analysis (2007S)

Selected topics in applied analysis

6.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Details

Language: German

Lecturers

Karlheinz Gröchenig

Classes (iCal) - next class is marked with N

    
    Tuesday
    06.03.
    11:15 - 12:45
    Seminarraum
    
    Thursday
    08.03.
    11:15 - 12:45
    Seminarraum
    
    Tuesday
    13.03.
    11:15 - 12:45
    Seminarraum
    
    Thursday
    15.03.
    11:15 - 12:45
    Seminarraum
    
    Tuesday
    20.03.
    11:15 - 12:45
    Seminarraum
    
    Thursday
    22.03.
    11:15 - 12:45
    Seminarraum
    
    Tuesday
    27.03.
    11:15 - 12:45
    Seminarraum
    
    Thursday
    29.03.
    11:15 - 12:45
    Seminarraum
    
    Tuesday
    17.04.
    11:15 - 12:45
    Seminarraum
    
    Thursday
    19.04.
    11:15 - 12:45
    Seminarraum
    
    Tuesday
    24.04.
    11:15 - 12:45
    Seminarraum
    
    Thursday
    26.04.
    11:15 - 12:45
    Seminarraum
    
    Thursday
    03.05.
    11:15 - 12:45
    Seminarraum
    
    Tuesday
    08.05.
    11:15 - 12:45
    Seminarraum
    
    Thursday
    10.05.
    11:15 - 12:45
    Seminarraum
    
    Tuesday
    15.05.
    11:15 - 12:45
    Seminarraum
    
    Tuesday
    22.05.
    11:15 - 12:45
    Seminarraum
    
    Thursday
    24.05.
    11:15 - 12:45
    Seminarraum
    
    Thursday
    31.05.
    11:15 - 12:45
    Seminarraum
    
    Tuesday
    05.06.
    11:15 - 12:45
    Seminarraum
    
    Tuesday
    12.06.
    11:15 - 12:45
    Seminarraum
    
    Thursday
    14.06.
    11:15 - 12:45
    Seminarraum
    
    Tuesday
    19.06.
    11:15 - 12:45
    Seminarraum
    
    Thursday
    21.06.
    11:15 - 12:45
    Seminarraum
    
    Tuesday
    26.06.
    11:15 - 12:45
    Seminarraum
    
    Thursday
    28.06.
    11:15 - 12:45
    Seminarraum

Information

Aims, contents and method of the course

This course will develop the theory of pseudodifferential operators with time-frequency methods. Pseudodifferential operators are a
generalization of differential operators and have their most important application in the analysis of partial differential equations. The time-frequency approach is motivated by engineering
applications and also by quantum mechanics. Pseudodifferential operators occur under the name of time-varying systems and are used to model the transmission of signals.

Planned topics: Description of pseudodifferential operators by time-frequency representations

Time-varying systems and channel modelling

Modulation spaces and symbol classes for pseudodifferential operators

Boundedness of pseudodifferential operators

Algebras and invertibility of pseudodifferential operators.

Course language: To accomodate the students of the IK ``Time-frequency
analysis and microlocal analysis'', the course will be held in English.

This is a three credit course. Since I will be abroad for some time in
June, I will teach four hours per week during March, April, and May.

Assessment and permitted materials

Minimum requirements and assessment criteria

The goal of this course it to establish the formalism of
pseudodifferential operators, and to prove boundedness and invertibility results.

Examination topics

Methoden and prerequisites: good knowledge of harmonic analysis, basic facts about
time-frequency analysis. The course can be taken as a continuation of the course on time-frequency analysis in the winter semester 2006/07.

Reading list

Roland Steinbauer, ``Pseudodifferentialoperatoren &
Mikrolokale Analysis", Lecture notes, winter semester 2006/07.

G. Folland ``Harmonic Analysis on Phase Space'', Princeton Univ., 1989.

K. Gröchenig, ``Foundations of Time-Frequency Analysis'', Birkhäuser, Boston, 2001.

K. Gröchenig, ``A pedestrian's approach to pseudodifferential operators'', in ``Harmonic Analysis and Applications'', C. Heil, ed.,
Birkhäuser, 2006.

Association in the course directory

2.1. Lecture Courses, Tutorials, and Conversatoriums

25.02. Mathematics ➡ A. Diploma Programme

Last modified: Mo 07.09.2020 15:40