Resonance index and singular mu-invariant

Abstract

With the essential spectrum of a self-adjoint operator given a relatively trace class perturbation one can associate an integer-valued invariant which admits different descriptions as the singular spectral shift function, total resonance index, and singular $\mu$-invariant. In this paper we give a direct proof of the equality of the total resonance index and singular $\mu$-invariant assuming only the limiting absorption principle. The proof is based on an application of the argument principle to the poles and zeros of the analytic continuation of the scattering matrix considered as a function of the coupling parameter.

10 pages

References in corpus (5)

• Absolutely continuous and singular spectral shift functions
• Infinitesimal spectral flow and scattering matrix
• Resonance index and singular spectral shift function
• Singular spectral shift function for Schrödinger operators
• A Topological Approach to Unitary Spectral Flow via Continuous Enumeration of Eigenvalues

Cited by in corpus (1)

• A remark on imaginary part of resonance points