# Note on the Fourier-Laplace Transform of $\overline{\partial}$-Cohomology Classes

### T. Hatziafratis

University of Athens, Greece

## Abstract

We construct the inverse of the Fourier-Laplace transform of $\overline{\partial}$-cohomology classes (of $(n, n–1)$-forms) in the complement of a convex compact set in $\mathbb C^n$, 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.

## Cite this article

T. Hatziafratis, Note on the Fourier-Laplace Transform of $\overline{\partial}$-Cohomology Classes. Z. Anal. Anwend. 17 (1998), no. 4, pp. 907–915

DOI 10.4171/ZAA/858