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We introduce the wave front set  with respect to the iterates of a hypoelliptic linear partial differential operator with constant coefficients of a classical distribution u in an open set Ω in the setting of ultradifferentiable classes of Braun, Meise, and\udTaylor. We state a version of the microlocal regularity theorem of Hormander for this new type of wave front set and give some examples and applications of the former result

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