We study resolvent estimates for a class of semiclassical pseudodifferential operators in the Euclidean space which are neither elliptic nor self-adjoint. Specifically, we assume that our operators have a finite number of doubly characteristic points. In the first part of the dissertation, we derive precise polynomial bounds on the resolvent in suitable regions inside the pseudospectrum, assuming that the quadratic approximations along the double characteristics are globally elliptic. In the second part of the dissertation, we weaken the assumption of global ellipticity and replace it with a dynamical averaging condition. Polynomial resolvent estimates are also derived in this case. Techniques based on transformations of FBI type play an important role throughout.
展开▼
