Representative function

In mathematics, in particular in the field of the representation theory of groups, a representative function is a function f on a compact topological group G obtained by composing a representation of G on a vector space V with a linear map from the endomorphisms of V into V 's underlying field. Representative functions arise naturally from finite-dimensional representations of G as the matrix-entry functions of the corresponding matrix representations. In mathematics, in particular in the field of the representation theory of groups, a representative function is a function f on a compact topological group G obtained by composing a representation of G on a vector space V with a linear map from the endomorphisms of V into V 's underlying field. Representative functions arise naturally from finite-dimensional representations of G as the matrix-entry functions of the corresponding matrix representations. It follows from the Peter–Weyl theorem that the representative functions on G are dense in the Hilbert space of square-integrable functions on G.