Wave front sets with respect to the iterates of an operator with constant coefficients. (English) Zbl 1472.47035
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 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.
MSC:
| 47F10 | Elliptic operators and their generalizations |
| 35H10 | Hypoelliptic equations |
| 46F05 | Topological linear spaces of test functions, distributions and ultradistributions |
Keywords:
hypoelliptic linear partial differential operator; microlocal regularity theorem; wave front setCitations:
Zbl 0735.46022References:
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