Does Levinson's theorem count complex eigenvalues ?

Abstract

Yes it does ! Indeed an extended version of Levinson's theorem is proposed for a system involving complex eigenvalues. The perturbed system corresponds to a realization of the Schroedinger operator with inverse square potential on the half-line, while the Dirichlet Laplacian on the half-line is chosen for the reference system. The resulting relation is an equality between the number of eigenvalues of the perturbed system and the winding number of the scattering system together with additional operators living at 0-energy and at infinite energy.

arXiv comment10 pages

References in corpus (4)

• On Schroedinger operators with inverse square potentials on the half-line
• Levinson's theorem for Schroedinger operators with point interaction: a topological approach
• The topological meaning of Levinson's theorem, half-bound states included
• Levinson's theorem and higher degree traces for Aharonov-Bohm operators