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

Semra Demirel

doi:10.1063/1.4746158

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arXiv · 1205.1772

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

Semra Demirel

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Abstract

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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BibTeX RIS

Semra Demirel. 2012-05-08. The spectral shift function and Levinson's theorem for quantum star graphs. https://doi.org/10.1063/1.4746158

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