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

We prove the following inclusion WF*(u)⊂ WF*(Pu)∪ Σ, u∈ε′* (Ω) where WF* denotes the non-quasianalytic Beurling or Roumieu wave front set, Ω is an open subset of R{double-struck} n, P is a linear partial differential operator with suitable ultradifferentiable coefficients, and Σ 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. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.The research of the second author was partially supported by MEC and FEDER, Project MTM2007-62643, and MEC, Project MTM2007-30904-E, and Conselleria d'Educacio de la GVA, Ajuda complementaria ACOMP 2009/253, Project GV/2010/040, and Universidad Politecnica de Valencia, Project Ref. 2773.Albanese, AA.; Jornet Casanova, D.; Oliaro, A. (2012). Wave front sets for ultradistribution solutions of linear partial differential operators with coefficients in non-quasianalytic classes. Mathematical News / Mathematische Nachrichten. 285(4):411-425. doi:10.1002/mana.201010039S411425285