Semiclassical hypoelliptic estimates for non-selfadjoint operators with double characteristics

Communications in Partial Differential Equations

Volumn 35, Issue 6, 2010, Pages 988-1028

  Hitrik, Michael ^a   Pravda Starov, Karel ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Double characteristics; Eigenvalues; Fbi bargmann transform; Hypoelliptic estimates; Non selfadjoint operators; Pseudodifferential calculus; Resolvent estimates; Singular space

Indexed keywords

EID: 77952485125     PISSN: 03605302     EISSN: 15324133     Source Type: Journal    
DOI: 10.1080/03605301003717092     Document Type: Article

References (15)

1. Hager, M., Sjöstrand, J. (2008). Eigenvalue asymptotics for randomly perturbed non-selfadjoint operators. Math. Ann. 342:177-243.
2. Hérau, F., Hitrik, M., Sjöstrand, J. (2008). Tunnel effect for Kramers-Fokker- Planck type operators. Ann. Henri Poincaré 9:209-274.
3. Hérau, F., Nier, F. (2004). Isotropic hypoellipticity and trend to equilibrium for the Fokker-Planck equation with a high degree potential. Arch. Ration. Mech. Anal. 171:151-218.
4. Hérau, F., Sjöstrand, J., Stolk, C. (2005). Semiclassical analysis for the Kramers-Fokker-Planck equation. Comm. PDE 30:689-760.
5. Hitrik, M., Pravda-Starov, K. (2009). Spectra and semigroup smoothing for non-elliptic quadratic operators. Math. Annalen. 344:801-846.
6. Hörmander, L. (1975). A class of hypoelliptic pseudodifferential operators with double characteristics. Math. Ann. 217:165-188.
7. Hörmander, L. (1985). The Analysis of Linear Partial Differential Operators, Vols. I-IV. Springer-Verlag.
8. Hörmander, L. (1995). Symplectic classification of quadratic forms, and general Mehler formulas. Math. Z. 219:413-449.
9. Pravda-Starov, K. (2008). Contraction semigroups of elliptic quadratic differential operators. Math. Z. 259:363-391.
10. Pravda-Starov, K. Subelliptic estimates for quadratic differential operators. To appear in Amer. J. Math.
11. Sjöstrand, J. (1974). Parametrices for pseudodifferential operators with multiple characteristics. Ark. för Matematik 12:85-130.
12. Sjöstrand, J. (1990). Geometric bounds on the density of resonances for semiclassical problems. Duke Math. J. 60:1-57.
13. Sjöstrand, J. (1996). Function spaces associated to global I-Lagrangian manifolds. In: Structure of Solutions of Differential Equations, Katata/Kyoto, 1995. River Edge, NJ: World Science Publishers, pp. 369-423.
14. Sjöstrand, J. Resolvent estimates for non-self-adjoint operators via semigroups. Preprint, http://arxiv.org/abs/0906.0094.
15. Sjöstrand, J., Zworski, M. (1995). The complex scaling method for scattering by strictly convex obstacles. Ark. for Matematik 33:135-172.