A new Levinson's theorem for potentials with critical decay.

Xiaoyao Jia (1) , François Nicoleau (2) , Xue Ping Wang (2)

1 University of Sciences and Technology
2 LMJL - Laboratoire de Mathématiques Jean Leray

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 for this class of potentials in presence of zero eigenvalue and zero resonance.

Mots clés: Levinson's theorem; Schrödinger operators; resolvent expansion; zero energy resonance; spectral shift function; Levinson's theorem.

Domaines: Théorie spectrale [math.SP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Xiaoyao Jia, François Nicoleau, Xue Ping Wang. A new Levinson's theorem for potentials with critical decay.. Annales Henri Poincaré, 2012, 13 (1), pp. 41-84. ⟨hal-00499429⟩