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We characterize the wave front set $WF^P_\ast(u)$ with respect to theiterates of a linear partial differential operator with constant coefficientsof a classical distribution $u\in{\mathcal D}'(\Omega)$, $\Omega$ an opensubset in ${\mathbb R}^n$. We use recent Paley-Wiener theorems for generalizedultradifferentiable classes in the sense of Braun, Meise and Taylor. We alsogive several examples and applications to the regularity of operators withvariable coefficients and constant strength. Finally, we construct adistribution 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