Mathematische Zeitschrift

, Volume 248, Issue 3, pp 593–633

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

Article

DOI: 10.1007/s00209-004-0673-9

Cite this article as:
Fournais, S. & Skibsted, E. Math. Z. (2004) 248: 593. doi:10.1007/s00209-004-0673-9

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesUniversité Paris-Sud-Bât 425Orsay CedexFrance
  2. 2.Institut for Matematiske FagAarhus UniversitetNy MunkegadeDenmark