Zero energy asymptotics of the resolvent for a class of slowly decaying potentials

Details Zero energy asymptotics of the resolvent for a class of slowly decaying potentials Zero energy asymptotics of the resolvent for a class of slowly decaying potentials

2003-06-20

arxiv.org/abs/math-ph/0306051v1

Physics

Mathematical Physics

45 pages

Scientific paper

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.

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