Semiclassical study of shape resonances in the Stark effect

Semiclassical behavior of Stark resonances is studied. The complex distortion outside a cone introduced to study in any energy region for the Hamiltonians with non-globally analytic potentials. non-trapping resolvent estimate proved by escape function method. Weyl law and resonance expansion propagator are shape model. To prove theorem, functional pseudodifferential calculus effect established, which also useful spectral shift function.