Quasianalytic wave front sets for solutions of linear partial differential operators
type: Item
instance of: scholarly article
title: Quasianalytic wave front sets for solutions of linear partial differential operators
zbMATH Open document ID: 1208.46037
published in: Integral Equations and Operator Theory
publication date: 2010-08-23T00:00:00Z
review text: The authors study the wave front set \(WF_*(u)\) of a distribution \(u\), where \(*\) stands for a quasianalytic or nonquasianalytic class of ultradifferentiable functions of Beurling or Roumieu type [in the sense of \textit{R.\,W.\thinspace Braun, R.\,Meise} and \textit{B.\,A.\thinspace Taylor}, Result.\ Math.\ 17, No.\, 3--4, 206--237 (1990; Zbl 0735.46022)]. It is proved that Hörmander's classical inclusion \(WF_*(u)\subset \Sigma\cup WF_*(Pu)\) also holds in this frame. Here, \(P\) is a differential operator with coefficients slightly more regular than the class \(*\) and \(\Sigma\) is the characteristic set of \(P\). The Beurling case is treated first and the Roumieu case is deduced from that, since the Roumieu wave front set \(WF_{\{\omega\}}(u)\) is the closure of the union of all Beurling wave front sets \(WF_{(\sigma)}(u)\) for all weights \(\sigma=o(\omega)\).
reviewed by: Michael Langenbruch
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 35A18
Mathematics Subject Classification ID: 35A21
zbMATH DE Number: 5774247
zbMATH Keywords: quasianalytic weight function
zbMATH Keywords: wave front set
zbMATH Keywords: propagation of singularities
zbMATH Keywords: kernel theorem
author: Angela A. Albanese
author: David Jornet
author: A. Oliaro
MaRDI profile type: Publication
full work available at URL: s00020-010-1742-6
OpenAlex ID: W2078085023
cites work: Regularite gevrey et iteres pour une classe d'operateurs hypoelliptiques
cites work: Q3478821
cites work: Q3593233
cites work: Q4497400
cites work: Nonradial Hörmander algebras of several variables and convolution operators
cites work: A comparison of two different ways to define classes of ultradifferentiable functions
cites work: Ultradifferentiable functions and Fourier analysis
cites work: Superposition in classes of ultradifferentiable functions
cites work: Pseudodifferential operators of Beurling type and the wave front set
cites work: A support theorem for quasianalytic functionals
cites work: Uniqueness theorems and wave front sets for solutions of linear differential equations with analytic coefficients
cites work: Q5673937
cites work: Q4340900
cites work: Concave majorants of positive functions
cites work: Almost analytic extension of ultradifferentiable functions and the boundary values of holomorphic functions
cites work: Q4274290
cites work: Acyclic inductive spectra of Fréchet spaces
cites work: Iterati di operatori e regolarita Gevrey microlocale anisotropa
DOI: 10.1007/S00020-010-1742-6
description: scientific article; zbMATH DE number 5774247