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

Abstract EN

We introduce the wave front set WF * P ( u ) with respect to the iterates of a hypoelliptic linear partial differential operator with constant coefficients of a classical distribution u ∈ ? ′ ( Ω ) 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.