About the holomorphic extension of CR functions on real hypersurfaces in complex space
type: Item
instance of: scholarly article
title: About the holomorphic extension of CR functions on real hypersurfaces in complex space
zbMATH Open document ID: 0564.32011
DOI: 10.1215/S0012-7094-84-05105-6
author: Mohamed Salah Baouendi
author: François Treves
published in: Duke Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: Without use of the method of analytic discs, the authors derive significant and general results on local holomorphic extensions of CR functions on a \(C^{\infty}\) hypersurface, \(\Sigma\), in \({\mathbb{C}}^{n+1}\). Suppose \(\Sigma\) is of finite type m (tangent to \({\mathbb{R}}^{2n+1}\) to order m) at 0. The authors prove the following results: (1) If m is odd then every CR function has an ambient holomorphic extension near 0. - (2) If m is even then every CR function has a holomorphic extension to at least one side of \(\Sigma\). These results follow from a deep analysis which first shows a sector property of Cauchy characteristics is sufficient for such extension results. Then the type conditions (even or odd) are shown to yield the appropriate sector properties.
Mathematics Subject Classification ID: 32V40
Mathematics Subject Classification ID: 32D15
zbMATH DE Number: 3899270
zbMATH Keywords: real hypersurfaces in complex space
zbMATH Keywords: CR distribution
zbMATH Keywords: local holomorphic extensions of CR functions
reviewed by: G. A. Harris
MaRDI profile type: Publication
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full work available at URL: s0012-7094-84-05105-6
OpenAlex ID: W1498167615
description: scientific article; zbMATH DE number 3899270