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Zeitschrift für Analysis und ihre Anwendungen


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Volume 17, Issue 4, 1998, pp. 907–915
DOI: 10.4171/ZAA/858

Published online: 1998-12-31

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

T. Hatziafratis

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.

Keywords: Fourier-Laplace transform, $\overline{\partial}$-cohomology classes

Hatziafratis T.: Note on the Fourier-Laplace Transform of $\overline{\partial}$-Cohomology Classes. Z. Anal. Anwend. 17 (1998), 907-915. doi: 10.4171/ZAA/858