Microfonctions I-lagrangiennes. (I-Lagrangian microfunctions)
type: Item
instance of: scholarly article
title: Microfonctions I-lagrangiennes. (I-Lagrangian microfunctions)
zbMATH Open document ID: 0659.46042
author: Jean-Marc Delort
author: Gilles Lebeau
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1988-01-01T00:00:00Z
review text: The singularities of some classes of distributions on \({\mathbb{R}}^ n\) which appear as solutions of semi-linear hyperbolic equations are studied. First, the authors study some generalization of Sjöstrand spaces \(H_{\psi}\) where the \(\psi\)-function is now assmed to be Lipschitz and subanalytic. Then they look at the singularities of distributions on \({\mathbb{R}}^ n\) which extend to a closed subanalytic subset F of \({\mathbb{C}}^ n\) containing \({\mathbb{R}}^ n\). They prove that such a distribution has its singular spectrum confined in the real part of the conormal bundle to F in \({\mathbb{C}}^ n\). From this they obtain a generalization of Kashiwara- Kawai's and Kashiwara-Shapira's result about \(\Pi (f_ j+i0)^{\lambda_ j}.\) All these results are closely related to the properties of subanalytic sets.
Mathematics Subject Classification ID: 46F20
Mathematics Subject Classification ID: 32B20
zbMATH DE Number: 4078024
zbMATH Keywords: solutions of semi-linear hyperbolic equations
zbMATH Keywords: Sjöstrand spaces
zbMATH Keywords: singularities of distributions
zbMATH Keywords: singular spectrum
zbMATH Keywords: conormal bundle
zbMATH Keywords: subanalytic sets
reviewed by: Yves Laurent
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4078024