Explicit version of the fundamental Ehrenpreis-Malgrange-Palamodov principle in the non-homogeneous case
type: Item
instance of: scholarly article
title: Explicit version of the fundamental Ehrenpreis-Malgrange-Palamodov principle in the non-homogeneous case
zbMATH Open document ID: 0886.46045
DOI: 10.1016/S0021-7824(97)89969-2
author: Stéphane Rigat
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1997-09-15T00:00:00Z
review text: Le but de cet article est de donner la forme explicite en termes de courants résiduels de toutes les solutions \(f\) d'un système d'équations aux dérivées partielles linéaires à coefficients constants dans un ouvert borné strictement convexe régulier de \(\mathbb{R}^n\): \[ P_j(i\partial/\partial t)f(t)=h_j(t), \qquad j=1,\dots,m \] tel que \(P:\mathbb{C}^n\to\mathbb{C}^m\) soit une application polynômiale intersection complète. Ce résultat est un prolongement direct de la version explicite du principe fondamental d'Ehrenpreis-Malgrange-Palamodov donnée par Berndtsson-Passare. Comme application directe du résultat, nous obtenons une nouvelle formule pour la solution du \(\overline{\partial}\) dans un ouvert régulier strictement convexe de \(\mathbb{C}^2\).
Mathematics Subject Classification ID: 46F10
zbMATH DE Number: 1060805
zbMATH Keywords: system of linear partial differential equation
zbMATH Keywords: Ehrenpreis-Malgrange-Palamodov principle
zbMATH Keywords: non-homogeneous case
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1060805