Removable singularities of holomorphic solution of linear partial differential equations
type: Item
instance of: scholarly article
title: Removable singularities of holomorphic solution of linear partial differential equations
zbMATH Open document ID: 1062.35009
author: Katasuju Igari
published in: Journal of the Mathematical Society of Japan
publication date: 2004-08-16T00:00:00Z
review text: The author considers Fuchsian linear partial differential operators in the complex domain, of the form: \[ P(z,D)=\left( \sum^r_{s=0} a_s(z) (z_1D_1)^{r-s} \right)D_n^{m-r}+ Q(z,D) \] where the lower order part \(Q(z,D)\) satisfies suitable Fuchs conditions. The coefficients \(a_s(z)\), \(z= (z_1,\dots,z_n) \in \mathbb{C}^n\), and the coefficients of \(Q(z,D)\) are assumed holomorphic in a neighborhood \(V\) of the origin. The problem under discussion is whether a solution \(u(z)\) of \(P(z,D)u=0\), holomorphic outside the characteristic hypersurface \(S\), has a holomorphic extension to the whole neighborhood \(V\), cf. \textit{K. Igari} [Funkc. Ekvacioj, Ser. Int. 37, 537--547 (1994; Zbl 0822.35003)]. In the present paper, new precise conditions for holomorphic extensions are given on the expression of \(P(z,D)\), with applications to the propagation of singularities for equations with noninvolutive double characteristics.
reviewed by: Luigi Rodino
Mathematics Subject Classification ID: 35A20
Mathematics Subject Classification ID: 35A10
Mathematics Subject Classification ID: 35A21
zbMATH DE Number: 2092009
zbMATH Keywords: Fuchsian linear partial differential operators
zbMATH Keywords: complex domain
zbMATH Keywords: noninvolutive double characteristics
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/1191418697
OpenAlex ID: W2077022964
DOI: 10.2969/JMSJ/1191418697
description: scientific article; zbMATH DE number 2092009