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Zbl 0711.35097
Gérard, Christian; Martinez, André
Prolongement méromorphe de la matrice de scattering pour des problèmes à deux corps à longue portée. (Meromorphic extension of the scattering matrix for long range two body problems). (French)
[J] Ann. Inst. Henri Poincaré, Phys. Théor. 51, No.1, 81-110 (1989). ISSN 0246-0211

Summary: We prove the existence of a meromorphic extension of the scattering matrix for long range potentials analytic at infinity. This extension exists as a bounded operator on some Gevrey spaces on $S\sp{n-1}$, with critical depending on the rate of decay of the potential at infinity. We use a semi-stationary definition of the scattering operator due to Isozaki-Kitada, using time dependent modifiers. We show that the poles of the scattering matrix coincide with the resonances of the Hamiltonian.

MSC 2000:: *35P25 Scattering theory (PDE)
81U05 2-body potential scattering theory
35J10 Schroedinger operator

Keywords: meromorphic extension; scattering matrix; long range potentials; Gevrey spaces; resonances

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