MPS-RR 2003-15
June 2003

Zero Energy Asymptotics of the Resolvent in the Long Range Case

by: Søren Fournais , Erik Skibsted

Abstract

We present a limiting absorption principle at zero energy for two-body Schrødinger operators with a long-range potential having a positive virial at infinity. Furthermore, we prove existence of limits (in weighted spaces), as the spectral parameter tends to zero, of all powers of the resolvent. The principal tools of proof are absence of eigenvalue at zero, singular Mourre theory and microlocal estimates. Some elements of the proof will be explained

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