A remark on a paper of E. B. Davies
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Abstract:
We explain the existence of open sets of complex quasi-modes in terms of Hörmander’s commutator condition.References
- E. B. Davies, Semi-classical states for non-self-adjoint Schrödinger operators, Comm. Math. Phys. 200 (1999), no. 1, 35–41. MR 1671904, DOI 10.1007/s002200050521
- J. J. Duistermaat and J. Sjöstrand, A global construction for pseudo-differential operators with non-involutive characteristics, Invent. Math. 20 (1973), 209–225. MR 344942, DOI 10.1007/BF01394095
- Victor Guillemin and Shlomo Sternberg, Geometric asymptotics, Mathematical Surveys, No. 14, American Mathematical Society, Providence, R.I., 1977. MR 0516965
- Lars Hörmander, Differential equations without solutions, Math. Ann. 140 (1960), 169–173. MR 147765, DOI 10.1007/BF01361142
- Lars Hörmander, The analysis of linear partial differential operators. III, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 274, Springer-Verlag, Berlin, 1985. Pseudodifferential operators. MR 781536
- Richard Melrose and Maciej Zworski, Scattering metrics and geodesic flow at infinity, Invent. Math. 124 (1996), no. 1-3, 389–436. MR 1369423, DOI 10.1007/s002220050058
Additional Information
- Maciej Zworski
- Affiliation: Department of Mathematics, Evans Hall, University of California, Berkeley, California 94720
- MR Author ID: 227055
- Email: zworski@math.berkeley.edu
- Received by editor(s): January 25, 2000
- Received by editor(s) in revised form: February 14, 2000
- Published electronically: March 14, 2001
- Communicated by: Christopher D. Sogge
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2955-2957
- MSC (2000): Primary 35Sxx, 81Q20
- DOI: https://doi.org/10.1090/S0002-9939-01-05909-3
- MathSciNet review: 1840099