Propagation of Gevrey singularities for solutions of linear differential operators with constant coefficients (Q5903204)

Let us consider a partial differential operator p(D) with constant coefficients. \textit{L. Hörmander} [Enseign. Math., II. Sér. 17, 99-163 (1971; Zbl 0224.35084)] investigated the propagation of \(C^{\infty}\)- singularities for solutions of the equation \(p(D)u=f\). In the present paper the author gives results on the propagation of singularities in the sense of Gevrey classes. The main theorem is stated by the use of the set L(p(D)) of localizations for the given operator p(D). The condition of the main theorem is the same as in the above mentioned paper by Hörmander, and hence the results in the present paper give a detailed version to the ones by Hörmander. A microlocalization of the main theorem can be shown [see also \textit{O. Liess} and \textit{R. Rosu}, Boll. Unione Mat. Ital., VI. Ser., B 3, 351-382 (1984; Zbl 0559.35009)].