Spectral projections and resolvent bounds for partially elliptic quadratic differential operators. (English) Zbl 1285.47049
The author studies resolvents and spectral projections for quadratic differential operators satisfying a partial ellipticity condition. Exponential-type resolvent bounds are established for these operators, which include Kramers-Fokker-Planck operators with quadratic potentials. For the norms of spectral projections of these operators, the author derives complete asymptotic expansions in dimension one while, for the case of arbitrary dimension, exponential upper bounds and the rate of exponential growth in a generic situation are obtained. Moreover, a complete characterization is given of those operators with orthogonal spectral projections onto the ground state.
Reviewer: Dian K. Palagachev (Bari)
MSC:
| 47F05 | General theory of partial differential operators |
| 35H20 | Subelliptic equations |
| 35P10 | Completeness of eigenfunctions and eigenfunction expansions in context of PDEs |
| 47A10 | Spectrum, resolvent |
| 35Q84 | Fokker-Planck equations |
Keywords:
non-selfadjoint operator; resolvent estimate; spectral projections; quadratic differential operator; FBI-Bargmann transform; Kramers-Fokker-Planck operatorReferences:
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