MPS-RR 2003-14
June 2003

Zero Energy Asymptotics of the Resolvent for a Class of Slowly Decaying Potentials

by: Søren Fournais , Erik Skibsted

Abstract

We prove a limiting absorption principle at zero energy for two-body Schrødinger 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

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This paper has now been published in Math. Z. 248, 593--633 (2004)