Loterre: Mathematics: Peter-Weyl theorem

mathematical analysis > functional analysis > transformation > harmonic analysis > Peter-Weyl theorem

algebra > group theory > topological group > compact group > Peter-Weyl theorem

algebra > representation theory > group representation > unitary representation > Peter-Weyl theorem

Peter-Weyl theorem

In mathematics, the Peter–Weyl theorem is a basic result in the theory of harmonic analysis, applying to topological groups that are compact, but are not necessarily abelian. It was initially proved by Hermann Weyl, with his student Fritz Peter, in the setting of a compact topological group G (Peter & Weyl 1927). The theorem is a collection of results generalizing the significant facts about the decomposition of the regular representation of any finite group, as discovered by Ferdinand Georg Frobenius and Issai Schur.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Peter%E2%80%93Weyl_theorem)

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