Microfonctions I-lagrangiennes. (I-Lagrangian microfunctions)
The singularities of some classes of distributions on \({\mathbb{R}}^ n\) which appear as solutions of semi-linear hyperbolic equations are studied. First, the authors study some generalization of Sjöstrand spaces \(H_{\psi}\) where the \(\psi\)-function is now assmed to be Lipschitz and subanalytic. Then they look at the singularities of distributions on \({\mathbb{R}}^ n\) which extend to a closed subanalytic subset F of \({\mathbb{C}}^ n\) containing \({\mathbb{R}}^ n\). They prove that such a distribution has its singular spectrum confined in the real part of the conormal bundle to F in \({\mathbb{C}}^ n\). From this they obtain a generalization of Kashiwara- Kawai's and Kashiwara-Shapira's result about \(\Pi (f_ j+i0)^{\lambda_ j}.\) All these results are closely related to the properties of subanalytic sets.
solutions of semi-linear hyperbolic equations
scientific article; zbMATH DE number 4078024