BulDML at Institute of Mathematics and Informatics >
IMI Periodicals >
Serdica Mathematical Journal >
2008 >
Volume 34, Number 1 >

Please use this identifier to cite or link to this item:

Title: Resolvent and Scattering Matrix at the Maximum of the Potential
Authors: Alexandrova, Ivana
Bony, Jean-François
Ramond, Thierry
Keywords: Scattering Matrix
Spectral Function
Schrödinger Equation
Fourier Integral Operator
Critical 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.
ISSN: 1310-6600
Appears in Collections:Volume 34, Number 1

Files in This Item:

File Description SizeFormat
2008-267-310.pdf610.91 kBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.


Valid XHTML 1.0!   Creative Commons License