Let E be a nonempty compact set with empty interior in the complex plane, and let U ⊆ C be a bounded open set such that U ∩ E = ∅ and ∂U = E. For instance, U might be the union of all of the bounded components of C\E. We are especially interested here in the situation where E is connected and U has infinitely many connected components, and moreover where each neighborhood of each element of E c...

Given a nite dimensional complex vector space V let D(V) denote the Weyl algebra of V. Kashiwara and Schapira ((KS96b]) constructed the conic sheaf O t V of holomorphic functions temperate at innnity and proved its invariance by the Laplace transform of D(V)-modules. Here we develop a similar program for the \dual" complex O w V of holomorphic functions rapidly decreasing at innnity.