A new Levinson's theorem for potentials with critical decay

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

2010-07-09

arxiv.org/abs/1007.1608v1

Mathematics

Spectral Theory

39 pp

Scientific paper

We study the low-energy asymptotics of the spectral shift function for
Schr\"odinger 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.

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