Resolvent and Scattering Matrix at the Maximum of the Potential

Alexandrova, Ivana, Bony, Jean-François, and Ramond, Thierry. "Resolvent and Scattering Matrix at the Maximum of the Potential." Serdica Mathematical Journal 34.1 (2008): 267-310. <http://eudml.org/doc/281490>.

@article{Alexandrova2008,
abstract = {2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38.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.},
author = {Alexandrova, Ivana, Bony, Jean-François, Ramond, Thierry},
journal = {Serdica Mathematical Journal},
keywords = {Scattering Matrix; Resolvent; Spectral Function; Schrödinger Equation; Fourier Integral Operator; Critical Energy; semi-classical Schrödinger operator; scattering matrix and amplitude},
language = {eng},
number = {1},
pages = {267-310},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Resolvent and Scattering Matrix at the Maximum of the Potential},
url = {http://eudml.org/doc/281490},
volume = {34},
year = {2008},
}

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
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 34
IS - 1
SP - 267
EP - 310
AB - 2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38.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.
LA - eng
KW - Scattering Matrix; Resolvent; Spectral Function; Schrödinger Equation; Fourier Integral Operator; Critical Energy; semi-classical Schrödinger operator; scattering matrix and amplitude
UR - http://eudml.org/doc/281490
ER -