Wednesday, May 9, 2012

1205.1772 (Semra Demirel)

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

Semra Demirel
We consider the Schr\"odinger 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.
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