03-294 S. Fournais and E. Skibsted

Zero energy asymptotics of the resolvent for a class of slowly decaying potentials (365K, PostScript) Jun 20, 03

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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.

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