Analytic factorization of Lie group representations

For every moderate growth representation (pi, E) of a real Lie group G on a Frechet space, we prove a factorization theorem of Dixmier-Malliavin type for the space of analytic vectors E(omega). There exists a natural algebra of superexponentially decreasing analytic functions A(G), such that E(omega) = Pi(A(G))E(omega). As a corollary we obtain that E(omega) coincides with the space of analytic vectors for the Laplace-Beltrami operator on G. (C) 2011 Elsevier Inc. All rights reserved.