Spherical matrix functions and Banach representability for compactly generated locally compact motion groups
Let \(G\) be a semidirect product of a compactly generated Abelian group \(S\) and a compact group \(K\); \(G\) is a compactly generated locally compact motion group. All topologically irreducible representations containing some element of the dual object \(\widehat K\) of \(K\) finitely many times are shown to be subquotients of \(\text{ind}_{S\uparrow G}\Lambda\) for some one-dimensional representation \(\Lambda\) of \(G\).
compactly generated locally compact motion group
scientific article; zbMATH DE number 1295047