Spectral projections and resolvent bounds for partially elliptic quadratic differential operators

Abstract

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.

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.com

References in corpus (2)

• Pseudospectra of semi-classical (pseudo)differential operators
• Non-elliptic quadratic forms and semiclassical estimates for non-selfadjoint operators

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• Kramers-Fokker-Planck operators with homogeneous potentials
• Global subelliptic estimates for Kramers-Fokker-Planck operators with some class of polynomials
• The relativistic rotated harmonic oscillator
• $L^p$-bounds for eigenfunctions of analytic non-self-adjoint operators with double characteristics