Wave Front Sets with respect to the Iterates of an Operator with Constant Coefficients

Abstract

We introduce the wave front set ${\text{WF}}_{*}^P(u)$ with respect to the iterates of a hypoelliptic linear partial differential operator with constant coefficients of a classical distribution $u\in {𝒟}^{\prime }(\Omega )$ in an open set Ω in the setting of ultradifferentiable classes of Braun, Meise, and Taylor. We state a version of the microlocal regularity theorem of Hörmander for this new type of wave front set and give some examples and applications of the former result.