2003 Prépublication d'Orsay numéro 2003- 45 (04/09/2003)



ZERO ENERGY ASYMPTOTICS OF THE RESOLVENT FOR A CLASS OF SLOWLY DECAYING POTENTIALS

FOURNAIS, Soeren - Analyse Numérique et E.D.P., Université Paris-Sud, Bât. 425, 91405 Orsay cedex
SKIBSTED, Erik - Analyse Numérique et E.D.P., Institut for Matematiske Fag, Aarhus Universitet, Ny Munkegade, 8000 Aarhus C, Denmark


Mots Clés : Scattering theory

Classification MSC : 81U05


Resumé :

Abstract :
We prove a limiting absorption principle at zero energy for two-body Schr\"odinger operators with long-range potentials having a positive virial at infinity. More precisely, we establish a complete asymptotic expansion of the resolvent in weighted spaces when the spectral parameter varies in cones; one of the two branches of boundary for the cones being given by the positive real axis. The principal tools are absence of eigenvalue at zero, singular Mourre theory and microlocal estimates.

Article : Fichier Postscript
Contact : soeren.fournais@math.u-psud.fr