Harmonic analysis on groups

Summary

Harmonic analysis on groups studies functions on a locally compact group by writing them as superpositions of basic oscillations attached to the group. For abelian groups the oscillations are the characters and the main tool is the Fourier transform on the dual group. For non-abelian groups the characters are replaced by irreducible unitary representations. The subject contains Fourier series, the Fourier transform on $\R^n$, and the representation theory of compact and Lie groups.