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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