Annales Henri Poincaré

, Volume 13, Issue 1, pp 41–84 | Cite as

A New Levinson’s Theorem for Potentials with Critical Decay

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Abstract

We study the low-energy asymptotics of the spectral shift function for Schrödinger operators with potentials decaying like \({O(\frac{1}{|x|^2})}\). We prove a generalized Levinson’s theorem for this class of potentials in presence of zero eigenvalue and zero resonance.

Keywords

Asymptotic Expansion Resonant State Zero Eigenvalue Trace Class Schwartz Kernel 
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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Xiaoyao Jia
    • 1
  • François Nicoleau
    • 2
  • Xue Ping Wang
    • 2
  1. 1.Department of MathematicsHenan University of Sciences and TechnologyLuoyangChina
  2. 2.Laboratoire de Mathématiques Jean Leray, UMR CNRS 6629Université de NantesNantes Cedex 3France

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