Wave front sets for ultradistribution solutions of linear partial differential operators with coefficients in non-quasianalytic classes

被引：11

作者：

Albanese, A. A. ^{[2
]}

Jornet, D. ^{[1
]}

Oliaro, A. ^{[3
]}

机构：

[1] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada IUMPA UPV, E-46022 Valencia, Spain

[2] Univ Salento, Dipartimento Matemat E De Giorgi, I-73100 Lecce, Italy

[3] Univ Turin, Dipartimento Matemat, I-10123 Turin, Italy

来源：

MATHEMATISCHE NACHRICHTEN | 2012年 / 285卷 / 04期

关键词：

Non-quasianalytic weight function; pseudodifferential operators; linear partial differential operators; wave front set; propagation of singularities; MSC (2010) Primary: 46F05; 35A18; 35A21; ULTRADIFFERENTIABLE FUNCTIONS; CONVOLUTION-OPERATORS; BEURLING TYPE;

D O I：

10.1002/mana.201010039

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the following inclusion WF*(u) subset of WF*(Pu) boolean OR Sigma, u is an element of epsilon(*)' (Omega), where WF* denotes the non-quasianalytic Beurling or Roumieu wave front set, Omega is an open subset of R-n, P is a linear partial differential operator with suitable ultradifferentiable coefficients, and S is the characteristic set of P. The proof relies on some techniques developed in the study of pseudodifferential operators in the Beurling setting. Some applications are also investigated. (C) 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：411 / 425

页数：15

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