Universität Wien
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250099 VO Harmonic analysis (2009W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: German

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 06.10. 11:00 - 13:00 Seminarraum
  • Thursday 08.10. 11:00 - 13:00 Seminarraum
  • Tuesday 13.10. 11:00 - 13:00 Seminarraum
  • Thursday 15.10. 11:00 - 13:00 Seminarraum
  • Tuesday 20.10. 11:00 - 13:00 Seminarraum
  • Thursday 22.10. 11:00 - 13:00 Seminarraum
  • Tuesday 27.10. 11:00 - 13:00 Seminarraum
  • Thursday 29.10. 11:00 - 13:00 Seminarraum
  • Tuesday 03.11. 11:00 - 13:00 Seminarraum
  • Thursday 05.11. 11:00 - 13:00 Seminarraum
  • Tuesday 10.11. 11:00 - 13:00 Seminarraum
  • Thursday 12.11. 11:00 - 13:00 Seminarraum
  • Tuesday 17.11. 11:00 - 13:00 Seminarraum
  • Thursday 19.11. 11:00 - 13:00 Seminarraum
  • Tuesday 24.11. 11:00 - 13:00 Seminarraum
  • Thursday 26.11. 11:00 - 13:00 Seminarraum
  • Tuesday 01.12. 11:00 - 13:00 Seminarraum
  • Thursday 03.12. 11:00 - 13:00 Seminarraum
  • Thursday 10.12. 11:00 - 13:00 Seminarraum
  • Tuesday 15.12. 11:00 - 13:00 Seminarraum
  • Thursday 17.12. 11:00 - 13:00 Seminarraum
  • Thursday 07.01. 11:00 - 13:00 Seminarraum
  • Tuesday 12.01. 11:00 - 13:00 Seminarraum
  • Thursday 14.01. 11:00 - 13:00 Seminarraum
  • Tuesday 19.01. 11:00 - 13:00 Seminarraum
  • Thursday 21.01. 11:00 - 13:00 Seminarraum
  • Tuesday 26.01. 11:00 - 13:00 Seminarraum
  • Thursday 28.01. 11:00 - 13:00 Seminarraum

Information

Aims, contents and method of the course

Fourier series, convergence of Fourier series
Theorem of Plancherel,
Poisson summation formula and sampling theory
Hilbert transform and L^p convergence of Fourier series
Fourier transform
convolution operators
Applications in PDEs and signal processing, possibly also in number theory

Assessment and permitted materials

Exam (oral)

Minimum requirements and assessment criteria

In this course, harmonic analysis will be understood as the theory of
Fourier series and the Fourier transform. The objective of the course
is to understand the principal concepts and results about Fourier
series and integrals. The basics of harmonic analysis form an
indispensible tools for many areas of analysis, including partial
differential equations, signal processing, analytic number theory,
etc.

Examination topics

Prerequisites: Analysis 1 - 3 and linear algebra

Reading list

Literatur: Buecher ueber harmonische Analyse oder Fourieranalyse von
I. Katznelson,
Deitmar,
Dym-McKean,
Grafakos,
Rudin,
Stein-Sakarchi,
Helson,
Vorlesungskriptum von R. Laugesen und C. Heil

Association in the course directory

MANV

Last modified: Mo 07.09.2020 15:40