Analytic factorization of Lie group representations

Abstract

For every moderate growth representation of a real Lie group G on a Frechet space E, we prove a factorization theorem of Dixmier--Malliavin type for the space of analytic vectors E^ω. There exists a natural algebra of superexponentially decreasing analytic functions A(G), such that E^ω = A(G) * E^ω. As a corollary we obtain that E^ωcoincides with the space of analytic vectors for the Laplace--Beltrami operator on G.

14 pages