Subelliptic Resolvent Estimates for Non-self-adjoint Semiclassical   Schrodinger Operators
  In this paper we prove a subelliptic resolvent estimate for a class of semiclassical non-self-adjoint Schr\"odinger operators with purely imaginary potentials when the spectral parameter is in a parabolic neighborhood of the imaginary axis. 
Ben Bellis
math.AP math.SP