Abstract
We adopt the canonical operator invented by Maslov (1972). It is an effective tool for constructing the global high frequency asymptotic to the solutions of the Laplace-Beltrami-Schrodinger equation. Maslov’s canonical operator is attached to an invariant Lagrangian submanifold in the phase space of the corresponding classical dynamical system (the generalized geodesic flow in our case). It carries functions defined on the Lagrangian submanifold in the glued cotangent bundle to those defined on the coordinate space.
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