David S. Shucker
Abstract
An elementary proof is given showing that if a continuous irreducible unitary representation of a locally compact unimodular group $G$ has one nontrivial square integrable matrix entry, then all its matrix entries are square integrable. This result was first proved by R. Godement.
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An elementary proof is given showing that if a continuous irreducible unitary representation of a locally compact unimodular group $G$ has one nontrivial square integrable matrix entry, then all its matrix entries are square integrable. This result was first proved by R. Godement.
Key concepts: Unimodular matrix, Square-integrable function, Integrable system, Mathematics, Square (algebra), Square matrix, Unitary state, Representation theory of SU