Microlocalization of Resonant States and Estimates of the Residue of the Scattering Amplitude

1. Aguilar, J., Combes, J.M.: A class of analytic perturbations for one-body Schrödinger Hamiltonians. Commun. Math. Phys. 22, 269–279 (1971)

   MATH  Google Scholar 

2. Bony, J.-F.: Résonances dans des domaines de taille h. Int. Math. Res. Notices (16), 817–847 (2001)

3. Bony, J.-F.: Résonances dans des petits domaines près d’une énergie critique. Ann. Henri Poincaré 3(4), 693–710 (2002)

   Article  MATH  Google Scholar 

4. Brummelhuis, R., Paul, T., Uribe, A.: Spectral estimates around a critical level. Duke Math. J. 78(3), 477–530 (1995)

   MATH  Google Scholar 

5. Burq, N.: Lower bounds for shape resonances widths of long range Schrödinger operators. Am. J. Math. 124(4), 677–735 (2002)

   MATH  Google Scholar 

6. Burq, N.: Semi-classical estimates for the resolvent in nontrapping geometries. Int. Math. Res. Not. (5), 221–241 (2002)

7. Dimassi, M., Sjöstrand, J.: Spectral asymptotics in the semi-classical limit. Cambridge: Cambridge University Press, 1999

8. Fujiié, S., Ramond, T.: Matrice de scattering et résonances associées à une orbite hétérocline. Ann. Inst. H. Poincaré Phys. Théor. 69(1), 31–82 (1998)

   Google Scholar 

9. Fujiié, S., Ramond, T.: Breit-wigner formula at barrier tops. Preprint 2002

10. Gérard, C., Martinez, A.: Prolongement méromorphe de la matrice de scattering pour des problèmes à deux corps à longue portée. Ann. Inst. H. Poincaré Phys. Théor. 51(1), 81–110 (1989)

    Google Scholar 

11. Gérard, C., Sjöstrand, J.: Semiclassical resonances generated by a closed trajectory of hyperbolic type. Commun. Math. Phys. 108(3), 391–421 (1987)

    Google Scholar 

12. Gérard, P.: Mesures semi-classiques et ondes de Bloch. Séminaire sur les Équations aux Dérivées Partielles, 1990–1991, École Polytech., Palaiseau, 1991, pp. Exp. No. XVI, 19

13. Helffer, B., Sjöstrand, J.: Résonances en limite semi-classique. Mém. Soc. Math. France (N.S.), no. 24-25, (1986)

14. Hunziker, W.: Distortion analyticity and molecular resonance curves. Ann. Inst. H. Poincaré Phys. Théor. 45(4), 339–358 (1986)

    MATH  Google Scholar 

15. Isozaki, H., Kitada, H.: Scattering matrices for two-body schrödinger operators. Sci. Papers College Arts Sci. Univ Tokyo 35(1), 81–107 (1985)

    MATH  Google Scholar 

16. Jecko, T.: From classical to semiclassical non-trapping behaviour: a new proof. Preprint Univ. Rennes 1 2002

17. Lahmar-Benbernou, A.: Estimation des résidus de la matrice de diffusion associés à des résonances de forme. I. Ann. Inst. H. Poincaré Phys. Théor. 71(3), 303–338 (1999)

    Google Scholar 

18. Lahmar-Benbernou, A., Martinez, A.: Semiclassical asymptotics of the residues of the scattering matrix for shape resonances. Asymptot. Anal. 20(1), 13–38 (1999)

    MATH  Google Scholar 

19. Lions, P.-L., Paul, T.: Sur les mesures de Wigner. Rev. Mat. Iberoamericana 9(3), 553–618 (1993)

    MATH  Google Scholar 

20. Martinez, A.: An introduction to semiclassical and microlocal analysis. New York: Springer-Verlag, 2002

21. Martinez, A.: Resonance free domains for non-globally analytic potentials. Ann. Henri Poincaré 3(4), 739–756 (2002)

    Article  MATH  Google Scholar 

22. Michel, L.: Semi-classical behavior of the scattering amplitude for trapping perturbations at fixed energy. Can. J. Math., to appear

23. Michel, L.: Semi-classical estimate of the residue of the scattering amplitude for long-range potentials. J. Phys. A 36, 4375–4393 (2003)

    Article  Google Scholar 

24. Petkov, V., Zworski, M.: Semi-classical estimates on the scattering determinant. Ann. Henri Poincaré 2(4), 675–711 (2001)

    MATH  Google Scholar 

25. Sjöstrand, J.: Singularités analytiques microlocales. Astérisque, Vol. 95, Paris: Soc. Math. France, 1982, pp. 1–166

26. Sjöstrand, J.: A trace formula and review of some estimates for resonances. In: Microlocal analysis and spectral theory (Lucca, 1996), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. 490, Dordrecht: Kluwer Acad. Publ., 1997, pp. 377–437

27. Sjöstrand, J.: Resonances for bottles and trace formulae. Math. Nachr. 221, 95–149 (2001)

    Article  MathSciNet  Google Scholar 

28. Sjöstrand, J., Zworski, M.: Complex scaling and the distribution of scattering poles. J. Am. Math. Soc. 4(4), 729–769 (1991)

    Google Scholar 

29. Stefanov, P.: Resonance expansions and Rayleigh waves. Math. Res. Lett. 8(1-2), 107–124 (2001)

30. Stefanov, P.: Estimates on the residue of the scattering amplitude. Asympt. Anal. 32(3,4), 317–333 (2002)

    Google Scholar 

31. Stefanov, P.: Sharp upper bounds on the number of resonances near the real axis for trapped systems. Am. J. Math. 125(1), 183–224 (2003)

    MATH  Google Scholar 

32. Tang, S-H., Zworski, M.: From quasimodes to reasonances. Math. Res. Lett. 5(3), 261–272 (1998)

    MATH  Google Scholar 

33. Tang, S-H., Zworski, M.: Resonance expansions of scattered waves. Comm. Pure Appl. Math. 53(10), 1305–1334 (2000)

    Article  MATH  Google Scholar 

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