We study resolvents and spectral projections for quadratic differential
operators under an assumption of partial ellipticity. We establish
exponential-type resolvent bounds for these operators, including
Kramers-Fokker-Planck operators with quadratic potentials. For the norms of
spectral projections for these operators, we obtain complete asymptotic
expansions in dimension one, and for arbitrary dimension, we obtain exponential
upper bounds and the rate of exponential growth in a generic situation. We
furthermore obtain a complete characterization of those operators with
orthogonal spectral projections onto the ground state.Comment: 60 pages, 3 figures. J. Pseudo-Differ. Oper. Appl., to appear.
Revised according to referee report, including minor changes to Corollary
1.8. The final publication will be available at link.springer.co
