The spectral shift function and Levinson's theorem for quantum star graphs

Abstract

We consider the Schrödinger operator on a star shaped graph with $n$ edges joined at a single vertex. We derive an expression for the trace of the difference of the perturbed and unperturbed resolvent in terms of a Wronskian. This leads to representations for the perturbation determinant and the spectral shift function, and to an analog of Levinson's formula.

References in corpus (2)

• Spectra of graph neighborhoods and scattering
• Levinson's theorem for graphs