UCLA

In this work we examine aspects of spectral theory for semiclassical non-self-adjoint Schrodinger operators.

First, we show a subelliptic resolvent estimate for spectral parameters in an

unbounded cubic neighborhood of the imaginary axis for a broad class of semiclassical Schrodinger operators with complex potentials of at most quadratic growth.

We then generalize this result by showing that the same type of resolvent estimate also holds for non-self-adjoint magnetic Schrodinger operators under suitable growth conditions

on the magnetic potential.

Lastly, we show how this resolvent estimate can be applied to yield a large time expansion for the semigroup generated by such an operator in terms of spectral data near the origin.