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

T. Hatziafratis

doi:10.4171/zaa/858

JournalszaaVol. 17, No. 4pp. 907–915

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

T. Hatziafratis
University of Athens, Greece

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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 $C^{n}$ , 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