Geodesic
Resolvent and Scattering Matrix at the Maximum of the Potential
Serdica Mathematical Journal, Tome 34 (2008) no. 1, pp. 267-310.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

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.
Keywords: Scattering Matrix, Resolvent, Spectral Function, Schrödinger Equation, Fourier Integral Operator, Critical Energy 
@article{SMJ2_2008_34_1_a10,
     author = {Alexandrova, Ivana and Bony, Jean-Fran\c{c}ois and Ramond, Thierry},
     title = {Resolvent and {Scattering} {Matrix} at the {Maximum} of the {Potential}},
     journal = {Serdica Mathematical Journal},
     pages = {267--310},
     publisher = {mathdoc},
     volume = {34},
     number = {1},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2008_34_1_a10/}
}
TY  - JOUR
AU  - Alexandrova, Ivana
AU  - Bony, Jean-François
AU  - Ramond, Thierry
TI  - Resolvent and Scattering Matrix at the Maximum of the Potential
JO  - Serdica Mathematical Journal
PY  - 2008
SP  - 267
EP  - 310
VL  - 34
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SMJ2_2008_34_1_a10/
LA  - en
ID  - SMJ2_2008_34_1_a10
ER  - 
%0 Journal Article
%A Alexandrova, Ivana
%A Bony, Jean-François
%A Ramond, Thierry
%T Resolvent and Scattering Matrix at the Maximum of the Potential
%J Serdica Mathematical Journal
%D 2008
%P 267-310
%V 34
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SMJ2_2008_34_1_a10/
%G en
%F SMJ2_2008_34_1_a10
Alexandrova, Ivana; Bony, Jean-François; Ramond, Thierry. Resolvent and Scattering Matrix at the Maximum of the Potential. Serdica Mathematical Journal, Tome 34 (2008) no. 1, pp. 267-310. http://geodesic.mathdoc.fr/item/SMJ2_2008_34_1_a10/