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

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Abstract.

We prove a limiting absorption principle at zero energy for two-body Schrödinger 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 tends to zero in cones which are adjacent to the positive real axis. The principal tools are absence of eigenvalue at zero, singular Mourre theory and microlocal estimates.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, Université Paris-Sud-Bât 425, F-91405, Orsay Cedex, France

    S. Fournais

  2. Institut for Matematiske Fag, Aarhus Universitet, Ny Munkegade, 8000, Aarhus C, Denmark

    E. Skibsted

Authors
  1. S. Fournais
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  2. E. Skibsted
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Correspondence to S. Fournais.

Additional information

in final form: 14 November 2003

S. Fournais was supported by a grant from the Carlsberg Foundation (before 31.12.02) and by a Marie Curie Fellowship of the European Community Programme ‘Improving the Human Research Potential and the Socio-Economic Knowledge Base’ under contract number HPMF-CT-2002-01822 (from 01.01.03).

E. Skibsted is (partially) supported by MaPhySto – A Network in Mathematical Physics and Stochastics funded by The Danish National Research Foundation.

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Fournais, S., Skibsted, E. Zero energy asymptotics of the resolvent for a class of slowly decaying potentials. Math. Z. 248, 593–633 (2004). https://doi.org/10.1007/s00209-004-0673-9

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