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A remark on a paper of E. B. Davies
Author(s):
Maciej
Zworski
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2955-2957.
MSC (2000):
Primary 35Sxx, 81Q20
Posted:
March 14, 2001
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Abstract:
We explain the existence of open sets of complex quasi-modes in terms of Hörmander's commutator condition.
References:
-
- 1.
- E.B. Davies, Semi-classical states for non-selfadjoint Schrödinger operators, Comm. Math. Phys. 200(1999), 35-41. MR 99m:34197
- 2.
- J.J. Duistermaat and J. Sjöstrand, A global construction for pseudo-differential operators with non-involutive characteristics, Inv. Math. 20(1973), 209-225. MR 49:9681
- 3.
- V.W. Guillemin and S. Sternberg, Geometrical Asymptotics, Mathematical Surveys, 14, Amer. Math. Soc., Providence, R.I., 1977. MR 58:24404
- 4.
- L. Hörmander, Differential equations without solutions, Math. Ann. 140(1960), 169-173. MR 26:5279
- 5.
- L. Hörmander, The Analysis of Linear Partial Differential Operators IV, Grundlehren der mathematischen Wissenschaften 275, Springer-Verlag, 1985. MR 87d:35002b
- 6.
- R.B. Melrose and M. Zworski, Scattering metrics and geodesic flow at infinity, Invent. Math. 124(1996), 389-436. MR 96k:58230
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Additional Information:
Maciej
Zworski
Affiliation:
Department of Mathematics, Evans Hall, University of California, Berkeley, California 94720
Email:
zworski@math.berkeley.edu
DOI:
10.1090/S0002-9939-01-05909-3
PII:
S 0002-9939(01)05909-3
Received by editor(s):
January 25, 2000
Received by editor(s) in revised form:
February 14, 2000
Posted:
March 14, 2001
Communicated by:
Christopher D. Sogge
Copyright of article:
Copyright
2001,
American Mathematical Society
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