Universität Wien

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

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

Last modified: Mo 07.09.2020 15:40