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Distributions spectrales pour des operateurs perturbes

Abstract : We describe a regularization of Birman-Krein theory for long range perturbations of the Laplacian. If the coefficients of the perturbation are not integrable, in partucular if they are L^2, we improve a result of Koplienko which proves the existence of a scattering phase that regularize the usual Birman-Krein spectral shift function. We give various semi-classical asymptotics for this regularized scattering phase as well as relations with scattering matrices and Fredholm determinants. Then, we apply these results to prove a "Levinson type" trace formula.
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https://tel.archives-ouvertes.fr/tel-00004025
Contributor : Jean-Marc Bouclet <>
Submitted on : Thursday, December 18, 2003 - 6:48:11 PM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
Long-term archiving on: : Friday, April 2, 2010 - 7:20:47 PM

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Jean-Marc Bouclet. Distributions spectrales pour des operateurs perturbes. Mathématiques [math]. Université de Nantes, 2000. Français. ⟨tel-00004025⟩

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