Harish-Chandra's regularity theorem (original) (raw)

In mathematics, Harish-Chandra's regularity theorem, introduced by Harish-Chandra, states that every invariant eigendistribution on a semisimple Lie group, and in particular every character of an irreducible unitary representation on a Hilbert space, is given by a locally integrable function. Harish-Chandra proved a similar theorem for semisimple p-adic groups.