Laplace hyperfunctions in several variables
In the 1980's Komatsu introduced a new class of hyperfunctions in one variable, called Laplace hyperfunctions, in order to consider the Laplace transform of a hyperfunction. The aim of the paper under review is to construct the sheaf of Laplace hyperfunctions in several variables and to study its fundamental properties. For that purpose, the authors establish an edge-of-the-wedge-type theorem for holomorphic functions of exponential type, which is the crucial step in the construction of the sheaf \(B_{\bar M}^{\exp}\) of Laplace hyperfunctions. The authors show pure \(n\)-codimensionality of the partial radial compactification \(\overline{\mathbb R^n}\times \mathbb C^m\) of \(\mathbb R^n\times \mathbb C^m\) relative to the sheaf \(\mathcal O^{\mathrm{exp}}_{\hat X}\) of holomorphic functions of exponential type, from which two important properties of \(B_{\bar M}^{\exp}\) follow: the softness of the sheaf \(B_{\bar M}^{\exp}\) and the extendability of the usual hyperfunctions to Laplace hyperfunctions.
scientific article; zbMATH DE number 6859846
scientific article