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

作者：Albanese A A; Jornet D^*; Oliaro A

来源：Mathematische Nachrichten, 2012, 285(4): 411-425.

DOI：10.1002/mana.201010039

• Non-quasianalytic weight function
• pseudodifferential operators
• linear partial differential operators
• wave front set
• propagation of singularities
• MSC (2010) Primary: 46F05
• 35A18
• 35A21

We prove the following inclusion %26lt;br%26gt;WF*(u) subset of WF*(Pu) boolean OR Sigma, u is an element of epsilon(*)%26apos; (Omega), %26lt;br%26gt;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.

• 出版日期2012-3