On holomorphic extension of hyperfunctions
type: Item
instance of: scholarly article
title: On holomorphic extension of hyperfunctions
zbMATH Open document ID: 0817.32004
DOI: 10.1007/BF00973473
author: M. Sh. Yakimenko
author: A. M. Kytmanov
published in: Siberian Mathematical Journal
publication date: 1994-11-08T00:00:00Z
review text: One of the consequences of the Bochner-Hartogs theorem is that every CR- function \(f\) defined on the boundary \(\partial \Omega\) of a bounded domain \(\Omega\) in \(\mathbb{C}^ n\) \((n > 1)\) is holomorphically extendable onto \(\Omega\) provided \(\partial \Omega\) is connected. In the case \(f\) is a hyperfunction on \(\partial \Omega\), the existence of a holomorphic extension was also proved. There is another generalization of the Bochner-Hartogs theorem, due to the author in collaboration with some others, which says that the function \(f\) needs only to be orthogonal to the Bochner-Martinelli kernels. In the present paper an analogue of this last version of the Bochner- Hartogs theorem is proved for the case of hyperfunctions.
Mathematics Subject Classification ID: 32A45
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32D15
zbMATH DE Number: 652220
zbMATH Keywords: integral representations
zbMATH Keywords: holomorphic extension
zbMATH Keywords: Bochner-Hartogs theorem
zbMATH Keywords: hyperfunctions
reviewed by: Ivan Pierre Ramadanoff
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00973473
OpenAlex ID: W2044205654
description: scientific article; zbMATH DE number 652220