We characterize the wave front set $WF^P_ast(u)$ with respect to the iterates of a linear partial differential operator with constant coefficients of a classical distribution $uinD'(Omega)$, $Omega$ an open subset in $R^n$. We use recent Paley-Wiener theorems for generalized ultradifferentiable classes in the sense of Braun, Meise and Taylor. We also give several examples and applications to the regularity of operators with variable coefficients and constant strength. Finally, we construct a distribution with prescribed wave front set of this type.

A characterization of the wave front set defined by the iterates of an operator with constant coefficients

BOITI, Chiara;
2017

Abstract

We characterize the wave front set $WF^P_ast(u)$ with respect to the iterates of a linear partial differential operator with constant coefficients of a classical distribution $uinD'(Omega)$, $Omega$ an open subset in $R^n$. We use recent Paley-Wiener theorems for generalized ultradifferentiable classes in the sense of Braun, Meise and Taylor. We also give several examples and applications to the regularity of operators with variable coefficients and constant strength. Finally, we construct a distribution with prescribed wave front set of this type.
2017
Boiti, Chiara; David, Jornet
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2263614
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