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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2000-32
August 2000

A unified approach to resolvent expansions at thresholds


Arne Jensen

Gheorghe Nenciu


Results are obtained on resolvent expansions around zero energyf or Schrýoedinger operators H = - Delta + V(x) on L^2(R^m), where V(x) is a sufficiently rapidly decaying real potential. The emphasis is on a unified approach, valid in all dimensions, which does not require one to distinguish between \int V(x) dx = 0 and \int V(x) \neq 0 in dimensions m=1,2. It is based on a factorization technique and repeated decomposition of the Lippmann-Schwinger operator. Complete results are given in dimensions m=1 and m=2.

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This paper has now been published in Rev. Math. Phys. 13 (2001), 717-754.