Resolvent and scattering matrix at the maximum of the potential

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dc.creatorAlexandrova, Ivana
dc.creatorBony, Jean-Francois
dc.creatorRamond, Thierry
dc.date2007-11-06
dc.date.accessioned2026-07-07T08:41:00Z
dc.date.available2026-07-07T08:41:00Z
dc.descriptionWe study the microlocal structure of the resolvent of the semi-classical Schrodinger operator with short range potential at an energy which is a unique non-degenerate global maximum of the potential. We prove that it is a semi-classical Fourier integral operator quantizing the incoming and outgoing Lagrangian submanifolds associated to the fixed hyperbolic point. We then discuss two applications of this result to describing the structure of the spectral function and the scattering matrix of the Schrodinger operator at the critical energy.
dc.description31 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/0711.0879
dc.identifierhttp://arxiv.org/abs/0711.0879
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141544
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.subject35P25;81U20;35S30;47A10;35B38
dc.titleResolvent and scattering matrix at the maximum of the potential
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