On the Laplace transform of a temperate distribution supported by a cone
Bent E. Petersen · Proceedings of the American Mathematical Society · 1972
The temperate distributions supported by a closed convex salient cone are characterized by explicit polynomial growth of the Laplace transform at infinity and at the boundary of the cylinder over the dual cone. This result is then used to characterize by their Laplace transforms the smooth kernels of degree λ − n \lambda - n where λ \lambda is positive.