Universität Wien
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562422 VO Banach algebras (2005S)

Banach algebra methods in applied analysis

0.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Details

Language: German

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 05.04. 13:00 - 15:00 Seminarraum
  • Wednesday 06.04. 13:00 - 15:00 Seminarraum
  • Tuesday 12.04. 13:00 - 15:00 Seminarraum
  • Wednesday 13.04. 13:00 - 15:00 Seminarraum
  • Tuesday 19.04. 13:00 - 15:00 Seminarraum
  • Wednesday 20.04. 13:00 - 15:00 Seminarraum
  • Tuesday 26.04. 13:00 - 15:00 Seminarraum
  • Wednesday 27.04. 13:00 - 15:00 Seminarraum
  • Tuesday 03.05. 13:00 - 15:00 Seminarraum
  • Wednesday 04.05. 13:00 - 15:00 Seminarraum
  • Tuesday 10.05. 13:00 - 15:00 Seminarraum
  • Wednesday 11.05. 13:00 - 15:00 Seminarraum
  • Wednesday 18.05. 13:00 - 15:00 Seminarraum
  • Tuesday 24.05. 13:00 - 15:00 Seminarraum
  • Wednesday 25.05. 13:00 - 15:00 Seminarraum
  • Tuesday 31.05. 13:00 - 15:00 Seminarraum
  • Wednesday 01.06. 13:00 - 15:00 Seminarraum
  • Tuesday 07.06. 13:00 - 15:00 Seminarraum
  • Wednesday 08.06. 13:00 - 15:00 Seminarraum
  • Tuesday 14.06. 13:00 - 15:00 Seminarraum
  • Wednesday 15.06. 13:00 - 15:00 Seminarraum
  • Tuesday 21.06. 13:00 - 15:00 Seminarraum
  • Wednesday 22.06. 13:00 - 15:00 Seminarraum
  • Tuesday 28.06. 13:00 - 15:00 Seminarraum
  • Wednesday 29.06. 13:00 - 15:00 Seminarraum

Information

Aims, contents and method of the course

Planned Topics:

1. Introduction to the theory of Banach algebras: Gelfand theory, Wiener's
Lemma

2. Algebras of infinite matrices

3. Frame theory, localized frames

4. Sampling theory

5. Time-Frequency analysis, Gabor frames

6. Pseudodifferential operators, Weyl calculus

Assessment and permitted materials

Minimum requirements and assessment criteria

The course will treat topics in applied harmonic analysis where methods from the theory of Banach algebras are useful. The applications will range from signal analysis to pseudodifferential operators.

Examination topics

Prerequisites: analysis, foundations of functional analysis (Hilbert and Banach spaces, linear operators), Fourier analysis (Fourier series and Fourier transform

Reading list

1. Conway, J. B., A course in functional analysis,
Springer, 1990. (für einführende Kapitel über Banachalgebren)

2. Gröchenig, K., Foundations of time-frequency analysis, Birkhäuser Boston, 2001. (für Frame-Theorie und Zeit-Frequenz-Analyse)

Association in the course directory

Last modified: Mo 07.09.2020 15:48