Edge-of-the-wedge theorem for elliptic systems
type: Item
instance of: scholarly article
title: Edge-of-the-wedge theorem for elliptic systems
zbMATH Open document ID: 0878.32013
author: Andrea D'Agnolo
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1997-12-07T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108372
review text: Let \(M\) be a real analytic manifold of dimension \(n\), \(N\subset M\) is a real submanifold of \(M\), and \(X\) and \(Y\) are their complexifications. \({\mathcal P}_X\) and \({\mathcal B}_M\) denote the sheaf of rings of linear holomorphic differential operators on \(X\) and the sheaf of Sato's hyperfunctions correspondingly. In the present paper an alternative proof is given of the Kashiwara-Kawai theorem for left coherent elliptic \({\mathcal P}_X\)-modules \({\mathcal M}\) for which \(Y\) is non characteristic, i.e. that \(H^j\mu_N(\text{R}{\mathcal H}\text{om}_{{\mathcal P_X}}({\mathcal M},^*)) = 0\), where \(^*={\mathcal A}_m\) or \({\mathcal B}_M\), \(\mu_N\) is the Sato microlocalization functor, and \(j<\text{cod}_MN\). It is also shown that the result fails to be true in higher dimensions for the sheaf \({\mathcal A}_M\) without the ellipticity requirement.
Mathematics Subject Classification ID: 32C38
Mathematics Subject Classification ID: 32C35
Mathematics Subject Classification ID: 32A45
Mathematics Subject Classification ID: 32V40
zbMATH DE Number: 889840
zbMATH Keywords: analytic manifold
zbMATH Keywords: sheaf of germs of holomorphic functions
zbMATH Keywords: holomorphic differential operators
zbMATH Keywords: hyperfunctions
zbMATH Keywords: microfunctions
reviewed by: Thomas V. Tonev
MaRDI profile type: Publication
cites work: On the boundary value problem for elliptic system of linear differential equations, I
cites work: Q3999005
cites work: The edge-of-the-wedge theorem for systems of constant coefficient partial differential operators. I, II
cites work: Q4403324
cites work: Q3202881
description: scientific article; zbMATH DE number 889840