Note on the Fourier-Laplace Transform of partial derivative-Cohomology Classes

We construct the inverse of the Fourier-Laplace transform of partial derivative-cohomology classes (of (n, n - 1)-forms) in the complement of a convex compact set in C-n, thus giving an analogue of the Borel transform (and its Polya representation) of entire functions of exponential type in several variables. The construction is based on a formula of Berndtsson.