We prove the following inclusion \[ WF_* (u)\subset WF_*(Pu)\cup \Sigma, \quad u\in\E^\prime_\ast(\Omega), \] 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 $\Sigma$ 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.
Wave front sets for ultradistribution solutions of linear partial differential operators with coefficients in non--quasianalytic classes
OLIARO, Alessandro
2012-01-01
Abstract
We prove the following inclusion \[ WF_* (u)\subset WF_*(Pu)\cup \Sigma, \quad u\in\E^\prime_\ast(\Omega), \] 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 $\Sigma$ 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.File in questo prodotto:
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