  For a real linear algebraic group G let A(G) be the algebra of analytic
vectors for the left regular representation of G on the space of
superexponentially decreasing functions. We present an explicit Dirac sequence
in A(G). Since A(G) acts on E for every Frechet-representation (\pi,E) of
moderate growth, this yields an elementary proof of a result of Nelson that the
space of analytic vectors is dense in E.

Representation Theory