  Let G be a solvable Lie group endowed with right Haar measure. We define and
study a dense Frechet *-subalgebra S of L1(G), consisting of smooth functions
rapidly-decreasing at infinity on G. When G is nilpotent, we recover the
classical Schwartz algebra introduced by R. Howe and other authors. We develop
a distribution theory for S, and we generalize the classical Kernel Theorem of
L. Schwartz to our setting.
