401-4427-70L Representation Theory in Signal Analysis

Abstract	The 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.
Learning objective
Content	The 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.
Prerequisites / Notice	Prerequisites: measure theory, topology, functional analysis, operator theory, Fourier analysis