Laplace hyperfunctions in several variables
type: Item
instance of: scholarly article
title: Laplace hyperfunctions in several variables
zbMATH Open document ID: 1401.32009
author: N. Honda
author: Kohei Umeta
published in: Journal of the Mathematical Society of Japan
publication date: 2018-04-13T00:00:00Z
review text: 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.
reviewed by: Nino Manjavidze
Mathematics Subject Classification ID: 32A45
Mathematics Subject Classification ID: 44A10
zbMATH DE Number: 6859846
zbMATH Keywords: hyperfunctions
zbMATH Keywords: Laplace transform
zbMATH Keywords: sheaf of Laplace hyperfunctions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/07017267
OpenAlex ID: W2963575646
cites work: Q5495379
cites work: Q3995750
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cites work: Vanishing theorems of cohomology groups with values in the sheaves O(inc,S) and O(dec)
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DOI: 10.2969/JMSJ/07017267
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description: scientific article; zbMATH DE number 6859846