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Bound on the number of eigenvalues near the boundary of the pseudospectrum
Author(s):
Mildred
Hager
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3867-3873.
MSC (2000):
Primary 34E10, 47G10, 47A75
Posted:
August 29, 2007
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Abstract:
We show an estimate of the number of eigenvalues in a neighbourhood of a finite part of the boundary of the semiclassical pseudospectrum of pseudodifferential non-selfadjoint operators in terms of a corresponding volume in phase space.
References:
-
- 1.
- E.B. Davies, Semiclassical states for Non-Self-Adjoint Schrödinger Operators, Commun. Math. Phys. 200 (1999), 35-41 MR 1671904 (99m:34197)
- 2.
- E.B. Davies, Pseudospectra of differential operators, J. Operator Theory 43 (2000), 243-262 MR 1753408 (2001b:47034)
- 3.
- N. Dencker, J. Sjöstrand, M. Zworski, Pseudospectra of semiclassical (pseudo-) differential operators, Comm. Pure Appl. Math. 57 (2004), 384-415 MR 2020109 (2004k:35432)
- 4.
- M. Dimassi, J. Sjöstrand, Spectral Asymptotics in the Semi-Classical Limit, London Math. Soc., Lecture Note Series 268, Cambridge University Press (1999) MR 1735654 (2001b:35237)
- 5.
- I.C. Gohberg, M.G. Krein, Introduction to the theory of linear nonselfadjoint operators, Translations of Mathematical Monographs 18, Amer. Math. Soc. (1969) MR 0246142 (39:7447)
- 6.
- M. Hager, Instabilité spectrale semiclassique d'opérateurs non-autoadjoints I: un exemple, Annales de la faculté des sciences de Toulouse no.2, volume 15 (2006), 195-232 MR 2244217
- 7.
- M. Hager, Instabilité spectrale semiclassique d'opérateurs non-autoadjoints II, Annales Henri Poincaré 7 (2006), 1035-1064. MR 2267057
- 8.
- B. Helffer, J. Sjöstrand, Résonances en limite semi-classique, Bulletin de la Soc. Math. France (1986)
- 9.
- J. Sjöstrand, Geometric bounds on the density of resonances for semiclassical problems, Duke Mathematical Journal 60 (1990), 1-57 MR 1047116 (91e:35166)
- 10.
- J. Sjöstrand, M. Zworski, Complex scaling and the distribution of scattering poles, Jour. Amer. Math. Soc. 4 (1991), 729-769 MR 1115789 (92g:35166)
- 11.
- J. Sjöstrand, Lectures on resonances, http://daphne.math.polytechnique.fr/~sjoestrand/
- 12.
- J. Sjöstrand, Resonances for bottles and trace formulae, Math. Nachr. 221 (2001), 95-149. MR 1806367 (2001k:58063)
- 13.
- E.C. Titchmarsh, The theory of functions, Oxford University Press (1939)
- 14.
- L.N. Trefethen, Pseudospectra of linear operators, SIAM Rev. 39 (1997), 383-406 MR 1469941 (98i:47004)
- 15.
- M. Zworski, A remark on a paper of E.B. Davies, Proceedings of the AMS 129 (1999), 2955-2957 MR 1840099 (2002e:35015)
- 16.
- M. Zworski, Numerical linear algebra and solvability of partial differential equations, Comm. Math. Phys. 229 (2002), 293-307 MR 1923176 (2003i:35008)
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Additional Information:
Mildred
Hager
Affiliation:
CMLS, Ecole polytechnique, 91128 Palaiseau Cédex, France, UMR 7640
Email:
mildred.hager@math.polytechnique.fr
DOI:
10.1090/S0002-9939-07-08914-9
PII:
S 0002-9939(07)08914-9
Keywords:
Pseudospectrum,
perturbation,
non-selfadjoint operators
Received by editor(s):
July 5, 2006
Received by editor(s) in revised form:
August 18, 2006
Posted:
August 29, 2007
Communicated by:
Mikhail Shubin
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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