Geodesic
The Spectrum of Resonances and the Trace Formula in a Potential Scattering Problem
Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 3, pp. 79-89

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For the wave equation with a potential perturbation, the localization and the asymptotic distribution of resonances, i.e., poles of the scattering matrix, are studied. To this end, it proves useful to exploit the relation between these poles and the spectrum of the corresponding Lax–Phillips semigroup. An explicit description of the generator of this semigroup is given. The regularized trace formula for the operators specifying the evolution of the initial data is applied to estimate how rarefied the spectrum of resonances can be.
Keywords: resonance, scattering matrix, Lax–Phillips semigroup
Mots-clés : trace formula. 
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     title = {The {Spectrum} of {Resonances} and the {Trace} {Formula} in a {Potential} {Scattering} {Problem}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2004_38_3_a6/}
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S. A. Stepin. The Spectrum of Resonances and the Trace Formula in a Potential Scattering Problem. Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 3, pp. 79-89. http://geodesic.mathdoc.fr/item/FAA_2004_38_3_a6/