Editing Regular representation (section)

==Topological group case==

For a topological group ''G'', the regular representation in the above sense should be replaced by a suitable space of functions on ''G'', with ''G'' acting by translation. See [[Peter–Weyl theorem]] for the [[Compact space|compact]] case. If ''G'' is a Lie group but not compact nor [[abelian group|abelian]], this is a difficult matter of [[harmonic analysis]]. The [[locally compact]] abelian case is part of the [[Pontryagin duality]] theory.