Wave front sets with respect to the iterates of an operator with constant coefficients
Summary: 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 \(u \in \mathcal{D}'(\Omega)\) in an open set \(\Omega\) in the setting of ultradifferentiable classes of \textit{R. W. Braun} et al. [Result. Math. 17, No. 3--4, 206--237 (1990; Zbl 0735.46022)]. 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.
hypoelliptic linear partial differential operator
scientific article; zbMATH DE number 7022396
scientific article