250099 VO Harmonic analysis (2009W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: German

Lecturers

Karlheinz Gröchenig

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