Harmonic Analysis

Basic topics in Fourier analysis on locally compact groups, in particular abelian groups: Haar measure, convolution, characters, the dual group, Fourier transform, Parseval's theorem, Plancherel theorem, Pontryagin duality theorem, inversion theorem, Bochener's theorem. Other topics such as harmonic analysis on compact or non-albian locally compact groups, Peter-Weyl theorem, amenability, probabilistic methods in harmonic analysis.