A topological group is a natural amalgam of topological spaces and groups: it is a Hausdorff space with continuous group operations. Topology adds a new flavour to representation theory. Especially interesting are compact groups, where group-invariant probability measures exist. Moreover, nice-enough functions on a compact group have Fourier series expansions, which generalise the classical Fourier series of periodic functions.
KeywordsFourier Series Topological Group Compact Group Unitary Representation Haar Measure
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