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Multiplicity of Resonances in Black Box Scattering

Published online by Cambridge University Press:  20 November 2018

L. Nedelec
L. Nedelec*
Affiliation:
L.A.G.A., Institut Galilée Université de Paris Nord av. J.B. Clement, F-93430 Villetaneuse, France, e-mail: nedelec@math.univ-paris13.fr
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Abstract

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We apply the method of complex scaling to give a natural proof of a formula relating the multiplicity of a resonance to the multiplicity of a pole of the scattering matrix.

Keywords

35P25

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 3 , 01 September 2004 , pp. 407 - 416
Copyright
Copyright © Canadian Mathematical Society 2004

References

[1] Agmon, S., A perturbation theory of resonances. Comm. Pure Appl. Math. 51 (1998), 1255–1309.Google Scholar
[2] Birman, M. S. and Krein, M. G., On the theory of wave operators and scattering operators. Dokl. Akad. Nauk SSSR 144 (1962), 475–478.Google Scholar
[3] Borthwick, D. and Perry, P., Scattering poles for asymptotically hyperbolic manifolds. Trans.Amer. Math. Soc. 354 (2001), 1215–1231.Google Scholar
[4] Christiansen, T., Spectral asymptotics for compactly supported perturbations of the Laplacian on Rn. Comm. Partial Differential Equations 23 (1998), 933–948.Google Scholar
[5] Dimassi, M. and Sjöstrand, J., Spectral asymptotics in the semi-classical limit. Lecture Note Series 268, Cambridge University Press, Cambridge, 1999.Google Scholar
[6] Gohberg, I. C. and Sigal, E. I., An operator generalization of the logarithmic residue theorem and Rouché's theorem. Mat. Sb. 84 (1971), 607–629.Google Scholar
[7] Helffer, B. and Sjöstrand, J., Analyse semi-classique pour l’équation de Harper. Mém. Soc. Math. France 34(1988).Google Scholar
[8] Jensen, A., Resonances in an abstract analytic scattering theory. Ann. Inst. H. Poincaré Physique theorique 33 (1980), 209–223.Google Scholar
[9] Klopp, F. and Zworski, M., Generic simplicity of resonances. Helv. Phys. Acta 68 (1995), 531–538.Google Scholar
[10] Petkov, V. and Zworski, M., Semi-classical estimates on the scattering determinant. Ann. Henri Poincaré 2 (2001), 675–711.Google Scholar
[11] Robert, D. and Tamura, H., Semiclassical estimates for resolvents and asymptotics for total scattering cross-sections. Ann. Inst. Henri Poincaré 46 (1987), 415–442.Google Scholar
[12] Sjöstrand, J., A trace formula and review of some estimates for resonances. NATO Adv. Sci. Inst. Ser. C 490 (1997), 377–437.Google Scholar
[13] Sjöstrand, J., Resonances for bottles and trace formulae. Math. Nachr. 221 (2001), 95–149.Google Scholar
[14] Sjöstrand, J. and Zworski, M., Complex scaling and the distribution of scattering poles. J. Amer. Math. Soc. 4 (1991), 729–769.Google Scholar
[15] Guillop, L. and Zworski, M., Scattering asymptotics for Riemann surfaces. Ann.Math. 145 (1997), 597–660.Google Scholar