\(\omega\)-hypoelliptic differential operators of constant strength
type: Item
instance of: scholarly article
title: \(\omega\)-hypoelliptic differential operators of constant strength
zbMATH Open document ID: 1058.35066
author: Antonio Galbis
author: Carmen Fernández
author: David Jornet
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-10-12T00:00:00Z
review text: The authors study the hypoellipticity of differential operators with constant strength and coefficients in \(E_\omega(\Omega)\), where \(\omega\) is a weight function. They show that any such operator which is homogeneous \(\omega\)-hypoelliptic is also \(\sigma\)-hypoelliptic for weight function \(\sigma= O(\omega)\). They also present a sufficient condition to ensure that a differential operator admits a parametrix. As a consequence they obtain some conditions on the weights \((\omega, G)\) to conclude that, for any operator \(P(x,D)\) with constant strength, the \(\sigma\)-hypoellipticity of the frozen operator \(P(x_0,D)\) implies the \(\omega\)-hypoellipticity of \(P(x,D)\). They include an example of an \(\omega\)-hypoelliptic operator which has not constant strength.
Mathematics Subject Classification ID: 35H10
zbMATH DE Number: 2107207
zbMATH Keywords: Ultradistribution
reviewed by: Viorel Iftimie
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.03.028
OpenAlex ID: W2090196520
cites work: A property of the functions and distributions annihilated by a locally integrable system of complex vector fields
cites work: Linear partial differential operators and generalized distributions
cites work: Q4497400
cites work: Ultradifferentiable functions and Fourier analysis
cites work: Analytic-gevrey hypollipticity for a class of pswudo-differential operators with multiple characteristics
cites work: Pseudodifferential operators on non-quasianalytic classes of Beurling type
cites work: Q4713497
cites work: Q3671563
cites work: On interior regularity of the solutions of partial differential equations
cites work: Q3344593
cites work: Q5606075
cites work: Q3222656
cites work: Sur une classe d'opérateurs différentiels hypoelliptiques
cites work: Whitney's extension theorem for ultradifferentiable functions of Beurling type
cites work: Gevrey-hypoelliptic operators which are not \(C^{\infty}\)-hypoelliptic
cites work: Q3693907
cites work: Q4274290
cites work: Q3966497
cites work: Q5528072
cites work: On hypoelliptic differential operators of constant strength
cites work: Gelfand Theory of Pseudo Differential Operators and Hypoelliptic Operators
cites work: Pseudodifferential operators of infinite order and Gevrey classes
DOI: 10.1016/J.JMAA.2004.03.028
Recommended article: Q4884252
Recommended article: Hypoelliptic differential operators with generalized constant coefficients
Recommended article: Q3006081
Recommended article: Q3728452
Recommended article: STRICTLY HYPOELLIPTIC OPERATORS WITH CONSTANT COEFFICIENTS
Recommended article: Differential operators with constant coefficients of hyperbolic- (hypo)elliptic type
Recommended article: Lower bounds for polynomials of many variables
Recommended article: Q3646918
Recommended article: On hypoellipticity for a class of pseudo-differential operators
Recommended article: Q5589554
description: scientific article; zbMATH DE number 2107207