Wave front sets for ultradistribution solutions of linear partial differential operators with coefficients in non‐quasianalytic classes
Identifieur interne : 000751 ( Main/Curation ); précédent : 000750; suivant : 000752Wave front sets for ultradistribution solutions of linear partial differential operators with coefficients in non‐quasianalytic classes
Auteurs : A. A. Albanese [Italie] ; D. Jornet [Espagne] ; A. Oliaro [Italie]Source :
- Mathematische Nachrichten [ 0025-584X ] ; 2012-03.
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Abstract
We prove the following inclusion \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty} $$ WF_* (u)\subset WF_*(Pu)\cup \Sigma , \quad u\in \mathcal {E}^\prime _\ast (\Omega ), $$ \end{document} where WF* denotes the non‐quasianalytic Beurling or Roumieu wave front set, Ω is an open subset of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {R}^n$\end{document}, 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.
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DOI: 10.1002/mana.201010039
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<front><div type="abstract" xml:lang="en">We prove the following inclusion \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty} $$ WF_* (u)\subset WF_*(Pu)\cup \Sigma , \quad u\in \mathcal {E}^\prime _\ast (\Omega ), $$ \end{document} where WF* denotes the non‐quasianalytic Beurling or Roumieu wave front set, Ω is an open subset of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {R}^n$\end{document}, 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.</div>
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