Function spaces associated to global \(I\)-Lagrangian manifolds. (English) Zbl 0889.46027

Sjöstrand, Johannes

Morimoto, M. (ed.) et al., Structure of solutions of differential equations. Proceedings of the Taniguchi symposium, Katata, Japan, June 26-30, 1995 and the RIMS symposium, Kyoto, Japan, July 3-7, 1995. Singapore: World Scientific. 369-423 (1996).

Summary: The author develops a theory for function spaces associated to certain classes of globally defined \(I\)-Lagrangian manifolds. He hopes that this theory will be useful in studying phase space tunneling and related problems in semiclassical analysis where complex trajectories are expected to play a role. The methods involve iteration of Fourier integral operators with exponentially very small errors and lead to integrals in high dimension.
For the entire collection see [Zbl 0882.00037].

MSC:

46E10	Topological linear spaces of continuous, differentiable or analytic functions
81Q20	Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory

Keywords:

function spaces; globally defined \(I\)-Lagrangian manifolds; phase space tunneling; semiclassical analysis; complex trajectories; iteration of Fourier integral operators; exponentially very small errors; integrals in high dimension