Gustav Zickert: A crash course on Fourier analysis on groups

Perhaps the most basic result in Fourier analysis is that the functions $e_n = e^{inx}$ form an ON-basis for $L^2(\mathbb{T})$.

The Peter-Weyl theorem gives an analogous result for the space $L^2(G)$, where $G$ is an arbitrary compact group. In this talk I will sketch a proof of this theorem, in the special case when $G$ is a compact matrix group.