On multi-products of pseudo-differential operators in Gevrey classes and its application to Gevrey hypoellipticity
type: Item
instance of: scholarly article
title: On multi-products of pseudo-differential operators in Gevrey classes and its application to Gevrey hypoellipticity
zbMATH Open document ID: 0587.35017
author: Kazuo Taniguchi
published in: Proceedings of the Japan Academy. Series A
publication date: 1985-01-01T00:00:00Z
review text: The author studies the Gevrey hypoellipticity of differential operators. For this he constructs the parametrices and investigates the relevant classes of pseudo-differential operators. For example, if \(P(x,D)=x^ 4_ 2(iD_ 1+D^ 2_ 2)+1\) in \(R^ 2\), then \(WF_{G(2)}(Pu)=WF_{G(2)}(u)\), and if \(P_ 1(x,D)=D^ 2_ 1+a(x_ 1)D^ 2_ 2+D^ 2_ 3\) in \(R^ 3\) where \(a\in G_{(k+1)/k}(R)\), \(a(t)=t^{2k}\) for \(| t| \leq 1\), \(| a(t)| \leq 1\) for \(| t| \leq 2\), then \(WF_{G(k+1)}(P_ 1u)=WF_{G(k+1)}(u)\).
Mathematics Subject Classification ID: 35H10
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 35A22
zbMATH DE Number: 3942027
zbMATH Keywords: Gevrey hypoellipticity
zbMATH Keywords: pseudo-differential operators
MaRDI profile type: Publication
full work available at URL: pjaa.61.291
OpenAlex ID: W1995847430
cites work: Nonanalytic-hypoellipticity for some degenerate elliptic operators
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cites work: Q5552928
cites work: Editorial board
cites work: Propagation of wave front sets of solutions of the Cauchy problem for hyperbolic equations in Gevrey classes
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cites work: Q3709218
DOI: 10.3792/PJAA.61.291
description: scientific article; zbMATH DE number 3942027