401-4427-70L  Representation Theory in Signal Analysis

SemesterHerbstsemester 2020
DozierendeF. Bartolucci
Periodizitäteinmalige Veranstaltung
LehrspracheEnglisch


KurzbeschreibungThe scope of the course is to give an introduction to the theory of unitary representations of locally compact groups with a particular regard to the applications of this theory in signal analysis.
Lernziel
InhaltThe scope of the course is to give an introduction to the theory of
unitary representations of locally compact groups with a particular regard to
the applications of this theory in signal analysis. The course starts with an
overview of the measure theory on locally compact groups. Then, the fundamental
definitions and results in representation theory are presented (irreducible
unitary representations, Schur’s lemma, voice transforms, square-integrable
representations, reproducing formulae). We conclude the course showing that
some of the most important transforms in applied harmonic analysis such as the
Gabor transform, the wavelet transform and the shearlet transform are related
to square-integrable unitary representations.
Voraussetzungen / BesonderesPrerequisites: measure theory, topology, functional analysis, operator
theory, Fourier analysis