On the pseudospectrum of elliptic quadratic differential operators

Duke Mathematical Journal

Volumn 145, Issue 2, 2008, Pages 249-279

  Pravda Starov, Karel ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 56349137118     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/00127094-2008-051     Document Type: Article

References (21)

1. L. S. BOULTON, Non-self-adjoint harmonic oscillator, compact semigroups and pseudospectra, J. Operator Theory 47 (2002), 413-429. MR 1911854
2. E. B. DAVIES, Spectral Theory and Differential Operators, Cambridge Stud. Adv. Math. 42, Cambridge Univ. Press, Cambridge, 1995. MR 1349825
3. -, Pseudo-spectra, the harmonic oscillator and complex resonances, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 455 (1999), 585-599. MR 1700903
4. -, Semi-classical states for non-self-adjoint Schrödinger operators, Comm. Math. Phys. 200 (1999), 35-41. MR 1671904
5. N. DENCKER, J. SJÖSTRAND, and M. ZWORSKI, Pseudospectra of semiclassical (pseudo-) differential operators, Comm. Pure Appl. Math. 57 (2004), 384-415. MR 2020109
6. n with bounded symbols (in Russian), Funkcional Anal. i Priložen 4, no. 4 (1970), 37-50; English translation in Functional Anal. Appl. 4 (1970), 202-212. MR 0270214
7. M. HITRIK, Boundary spectral behavior for semiclassical operators in dimension one, Int. Math. Res. Not. 2004, no. 64, 3417-3438. MR 2101278
8. L. HÖRMANDER, A class of hypoelliptic pseudodifferential operators with double characteristics, Math. Ann. 217 (1975), 165-188. MR 0377603
9. -, The Analysis of Linear Partial Differential Operators, III, Grundlehren Math. Wiss., Springer, Berlin, 1985. MR 0781536
10. -, The Analysis of Linear Partial Differential Operators, IV, Grundlehren Math. Wiss., Springer, Berlin, 1985. MR 0781537
11. T. KATO, Perturbation Theory for Linear Operators, Classics Math., Springer, Berlin, 1995. MR 1335452
12. R. D. MOYER, Local solvability in two dimensions: Necessary conditions for the principle-type case, preprint, 1978.
13. K. PRAVDA-STAROV, A complete study of the pseudo-spectrum for the rotated harmonic oscillator, J. London Math. Soc. (2) 73 (2006), 745-761. MR 2241978
14. -, "Sur le pseudo-spectre de certaines classes d'opérateurs pseudo-différentiels non auto-adjoints" in Séminaire: Équations aux dérivées partielles, 2006-2007, Semin. Equ. Deriv. Partielles, École Polytech., Palaiseau, 2007, no. 15. MR 2385202
15. -, Contraction semigroups of elliptic quadratic differential operators, Math. Z. 259 (2008), 363-391. MR 2390087
16. -, Etude du pseudo-spectre d'opérateurs non auto-adjoints, Ph.D. dissertation, Université de Rennes 1, Rennes, France 2006.
17. S. ROCH and B. SILBERMANN, C*-algebra techniques in numerical analysis, J. Operator Theory 35 (1996), 241-280. MR 1401690
18. J. SJÖSTRAND, Parametrices for pseudodifferential operators with multiple characteristics, Ark. Mat. 12 (1974), 85-130. MR 0352749
19. L. N. TREFETHEN, Pseudospectra of linear operators, SIAM Rev. 39 (1997), 383-406. MR 1469941
20. L. N. TREFETHEN and M. EMBREE, Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators, Princeton Univ. Press, Princeton, 2005. MR 2155029
21. M. ZWORSKI, A remark on a paper of E. B. Davies, Proc. Amer. Math. Soc. 129 (2001), 2955-2957. MR 1840099 [22] -, Numerical linear algebra and solvability of partial differential equations, Comm. Math. Phys. 229 (2002), 293-307. MR 1923176