  We provide a necessary and sufficient condition for the representability of a
function as the classical multidimensional Laplace transform, when the support
of the representing measure is contained in some generalized semi-algebraic
set. This is done by employing a method of Putinar and Vasilescu [Putinar, M.
and Vasilescu, F.-H., Solving moment problems by dimensional extension, Ann. of
Math. (2) 149 (1999), no. 3, 1087-1107] for the corresponding multidimensional
moment problem.
