Microlocal analytic smoothing effect for the Schrödinger equation
The purpose of the work is to study the microlocal analytic smoothness of solutions of the initial value problem for the linear Schrödinger equation with variable coefficients. More precisely, the behavior at infinity of the initial data is related to the microlocal analytic smoothness of solutions. These results are extensions to the analytic case of those by \textit{W. Craig, T. Kappeler} and \textit{W. Strauss} [Commun. Pure Appl. Math. 48, No. 8, 769-860 (1995; Zbl 0856.35106)], which concern the \(C^\infty\)-case. Here, the method of proof relies on \textit{J. Sjöstrand} [Singularites analytiques microlocales. Astérisque 95, 1-166 (1982; Zbl 0524.35007)], and is entirely different from that of Craig, Kappeler, and Srauss.
scientific article; zbMATH DE number 1425251