Zworski, Maciej A remark on a paper of E. B. Davies. (English) Zbl 0981.35107 Proc. Am. Math. Soc. 129, No. 10, 2955-2957 (2001). Summary: We explain the existence of open sets of complex quasi-modes in terms of Hörmander’s commutator condition. The title applies to E. B. Davies [Commun. Math. Phys. 200, 35-41 (1999; Zbl 0921.47060)]. Cited in 24 Documents MSC: 35S05 Pseudodifferential operators as generalizations of partial differential operators 35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs 81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory Keywords:semi-classical pseudodifferential operators; semi-classical symbols; complex quasi-modes; Hörmander’s commutator condition Citations:Zbl 0921.47060 PDFBibTeX XMLCite \textit{M. Zworski}, Proc. Am. Math. Soc. 129, No. 10, 2955--2957 (2001; Zbl 0981.35107) Full Text: DOI References: [1] E. B. Davies, Semi-classical states for non-self-adjoint Schrödinger operators, Comm. Math. Phys. 200 (1999), no. 1, 35 – 41. · Zbl 0921.47060 [2] J. J. Duistermaat and J. Sjöstrand, A global construction for pseudo-differential operators with non-involutive characteristics, Invent. Math. 20 (1973), 209 – 225. · Zbl 0282.35071 [3] Victor Guillemin and Shlomo Sternberg, Geometric asymptotics, American Mathematical Society, Providence, R.I., 1977. Mathematical Surveys, No. 14. · Zbl 0364.53011 [4] Lars Hörmander, Differential equations without solutions, Math. Ann. 140 (1960), 169 – 173. · Zbl 0093.28903 [5] 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. Lars Hörmander, The analysis of linear partial differential operators. IV, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 275, Springer-Verlag, Berlin, 1985. Fourier integral operators. [6] Richard Melrose and Maciej Zworski, Scattering metrics and geodesic flow at infinity, Invent. Math. 124 (1996), no. 1-3, 389 – 436. · Zbl 0855.58058 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.