Asymptotic behavior of regularized scattering phases for long range perturbations
Journées équations aux dérivées partielles (2002), article no. 2, 12 p.

We define scattering phases for Schrödinger operators on ℝ d as limit of arguments of relative determinants. These phases can be defined for long range perturbations of the laplacian; therefore they can replace the spectral shift function (SSF) of Birman-Krein’s theory which can just be defined for some special short range perturbations (we shall recall this theory for non specialists). We prove the existence of asymptotic expansions for these phases, which generalize results on the SSF.

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     author = {Bouclet, Jean-Marc},
     title = {Asymptotic behavior of regularized scattering phases for long range perturbations},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
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     pages = {1--12},
     publisher = {Universit\'e de Nantes},
     year = {2002},
     doi = {10.5802/jedp.600},
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     url = {http://archive.numdam.org/articles/10.5802/jedp.600/}
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Bouclet, Jean-Marc. Asymptotic behavior of regularized scattering phases for long range perturbations. Journées équations aux dérivées partielles (2002), article  no. 2, 12 p. doi : 10.5802/jedp.600. http://archive.numdam.org/articles/10.5802/jedp.600/

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