Support of CR-hyperfunctions
type: Item
instance of: scholarly article
title: Support of CR-hyperfunctions
zbMATH Open document ID: 0664.32012
published in: Proceedings of the Japan Academy. Series A
publication date: 1988-01-01T00:00:00Z
review text: The aim of this paper is to present a possible shape of the support of CR functions on a generic CR submanifold. Let X be an m-dimensional complex manifold and let N be a k-codimensional, generic, CR, and real analytic submanifold (0\(\leq k\leq m)\). The complexification of N is denoted by Y. A hyperfunction h on N is called a CR function if it satisfies the tangential Cauchy-Riemann system \({\bar \partial}_ b\). A real analytic submanifold L of N is said to be totally characteristic if \(\sqrt{- 1}T^*_ LN\subset \sqrt{-1}T^*N\subset SS({\bar \partial}_ b).\) Here SS(\({\bar \partial}_ b)\) means the characteristic variety of \({\bar \partial}_ b\). Then we have the following theorem. Let \(h\) be a non-zero CR hyperfunction on N. If \(L=\sup p(h)\) is a real analytic submanifold of N, then L is totally characteristic.
reviewed by: Masakazu Muro
Mathematics Subject Classification ID: 32V40
Mathematics Subject Classification ID: 32W05
zbMATH DE Number: 4086039
zbMATH Keywords: tangential Cauchy Riemann equation
zbMATH Keywords: support of CR functions on a generic CR submanifold
zbMATH Keywords: real analytic submanifold
zbMATH Keywords: totally characteristic
zbMATH Keywords: CR hyperfunction
author: Shinichi Tajima
MaRDI profile type: Publication
full work available at URL: pjaa.64.239
OpenAlex ID: W1967062019
cites work: Q3849170
cites work: Q5542941
cites work: Q3743663
cites work: Q5673938
cites work: Analyse microlocale sur les variétés de Cauchy-Riemann et problème du prolongement des solutions holomorphes des équations aux dérivées partielles
DOI: 10.3792/PJAA.64.239
description: scientific article; zbMATH DE number 4086039