Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2590

 Title: Resolvent and Scattering Matrix at the Maximum of the Potential Authors: Alexandrova, IvanaBony, Jean-FrançoisRamond, Thierry Keywords: Scattering MatrixResolventSpectral FunctionSchrödinger EquationFourier Integral OperatorCritical Energy Issue Date: 2008 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Mathematical Journal, Vol. 34, No 1, (2008), 267p-310p Abstract: We study the microlocal structure of the resolvent of the semiclassical Schrödinger 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 semiclassical 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 Schrödinger operator at the critical energy. Description: 2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38. URI: http://hdl.handle.net/10525/2590 ISSN: 1310-6600 Appears in Collections: Volume 34, Number 1

Files in This Item:

File Description SizeFormat