Resonances for bottles and trace formulae

Mathematische Nachrichten

Volumn 221, Issue , 2001, Pages 95-149

  Sjöstrand, Johannes ^a  

^a ECOLE POLYTECHNIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18044399941     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/1522-2616(200101)221:1<95::AID-MANA95>3.0.CO;2-P     Document Type: Article

References (27)

1. AGUILAR, J., and COMBES, J. M.: A Class of Analytic Perturbations for One-Body Schrödinger Hamiltonians, Comm. Math. Phys. 22 (1971), 269-279
2. BALSLEV, E., and COMBES, J. M.: Spectral Properties of Many-Body Schrödinger Operators with Dilation Analytic Interactions, Comm. Math. Phys. 22 (1971), 280-294
3. BARDOS, C., GUILLOT, J. C., and RALSTON, J.: La Relation de Poisson pour l'Équation des Ondes dans un Ouvert non Borné, Comm PDE 7 (1982), 905-958
4. DIMASSI, M., and SJÖSTRAND, J.: Spectral Asymptotics in the Semi-Classical Limit, London Mathematical Society Lecture Note Series 268, Cambridge University Press, Cambridge, 1999
5. GOHBERG, I. C., and KREIN, M. G.: Introduction to the Theory of Nonselfadjoint Operators, Transl. of Math. Monographs 18, AMS, Providence, 1969
6. GRUBB, G.: Functional Calculus for Pseudodifferential Boundary Problems, Progress in Math. Vol. 65, 2nd ed., Birkhäuser 1996
7. GUILLOPÉ, L., and ZWORSKI, M.: Scattering Asymptotics for Riemann Surfaces, Ann. Math. 145 (1997), 597-660
8. HELFFER, B., and SJÖSTRAND, J.: Equation de Schrödinger avec Champ Magnétique et Équation de Harper, Springer Lecture Notes in Physics 345 (1989), 118-197
9. HELFFER, B., and SJÖSTRAND, J.: Résonances en Limite Semiclassique. Bull, de la SMF 114 (3), Mémoire 24/25 (1986)
10. R. MELROSE, Scattering Theory and the Trace of the Wave Group, J. Funct. An. 45 (1982), 429-440
11. PETKOV, V., and ZWORSKI, M.: Breit-Wigner Approximation and the Distribution of Resonances, Comm. Math. Phys. 204 (2) (1999), 329-351
12. POPOV, G.: On the Contribution of Degenerate Periodic Trajectories to the Wave-Trace, Comm. Math. Phys. 196 (2) (1998), 363-383
13. POPOV, G., and VODEV, G.: Resonances near the Real Axis for Transparent Obstacles, Comm. Math. Phys. 207 (2) (1999), 411-438
14. POPOV, G., and VODEV, G.: Distribution of Resonances and Local Energy Decay in the Transmission Problem, Asymptot. Anal. 19 (1999), no. 3-4, 253-265
15. REED, M., and SIMON, B.: Methods of Modern Mathematical Physics, I-IV, Academic Press, New-York, 1978
16. SJÖSTRAND, J.: A Trace Formula and Review of Some Estimates for Resonances. In: Microlocal Analysis and Spectral Theory, NATO ASI Series C, Vol. 490, p. 377-437, Kluwer, 1997
17. SJÖSTRAND, J., and ZWORSKI, M.: Complex Scaling and the Distribution of Scattering Poles, J. of AMS 4 (4) (1991), 729-769
18. SJÖSTRAND, J., and ZWORSKI, M.: Distribution of Scattering Poles near the Real Axis, Comm. PDE 17 (5-6) (1992), 1021-1035
19. SJÖSTRAND, J., and ZWORSKI, M.: Lower Bounds on the Number of Scattering Poles, II, J. Funct. An. 123 (2) (1994), 336-367
20. SJÖSTRAND, J., and ZWORSKI, M.: Lower Bounds on the Number of Scattering Poles, Comm. PDE 18 (5-6) (1993), 847-857
21. SJÖSTRAND, J., and ZWORSKI, M.: Asymptotic Distribution of Resonances for Convex Obstacles, Acta Math. 183 (2) (1999), 191-253
22. STEFANOV, P.: Quasimodes and Resonances: Sharp Lower Bounds, Duke Math. J. 99 (1) (1999), 75-92
23. STEFANOV, P., and VODEV, G.: Neumann Resonances in Linear Elasticity for an Arbitrary Body, Comm. Math. Phys. 176 (1996), 645-659
24. TANG, S. U., and ZWORSKI, M.: From Quasimodes to Resonances, Math. Res. Letters 5 (3) (1998), 261-272
25. VODEV, G.: On the Distribution of Scattering Poles for Perturbations of the Laplacian, Ann. Inst. Fourier 40 (1992), 625-635
26. VODEV, G.: Asymptotics on the Number of Scattering Poles for Degenerate Perturbations of the Laplacian, J. Funct. Anal. 138 (2) (1996), 295 -310
27. ZWORSKI, M.: Poisson Formula for Resonances in Even Dimensions, Asian J. Math. 2 (3) (1998), 609-617