Propagation of singularities for hyperbolic operators with transverse propagation cone
The author studies the propagation of singularities for hyperbolic pseudo-differential operators P(x,D) with multiple characteristics. Let us consider an operator P(x,D) such that the localization at the characteristic \(\rho\) (with multiplicity r) is strictly hyperbolic on the normal bundle \(\Sigma_{\Omega}\), the set of characteristics of order \(\Omega\). He shows that, if there are no singularities on the backward bicharacteristics with the limit point \(\rho\), then there is no singularity at \(\rho\). In the case where the characteristic set is the union of \(\Omega\) hypersurfaces through \(\rho\) with linearly independent normals, he proves, under some conditions on the rank of the symplectic form, that if there are no singularities on the backward characteristic curves passing through \(\rho\) of these surfaces, then there is none at \(\rho\).
scientific article; zbMATH DE number 4179934