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arXiv · 1404.0001

Trace formulae for Schrodinger operators on metric graphs with applications to recovering matching conditions

Yulia Ershova·Alexander V. Kiselev
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Abstract

The paper is a continuation of the study started in \cite{Yorzh1}. Schrodinger operators on finite compact metric graphs are considered under the assumption that the matching conditions at the graph vertices are of $δ$ type. Either an infinite series of trace formulae (provided that edge potentials are infinitely smooth) or a finite number of such formulae (in the cases of $L_1$ and $C^M$ edge potentials) are obtained which link together two different quantum graphs under the assumption that their spectra coincide. Applications are given to the problem of recovering matching conditions for a quantum graph based on its spectrum.

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Yulia Ershova, Alexander V. Kiselev. 2014-03-29. Trace formulae for Schrodinger operators on metric graphs with applications to recovering matching conditions. https://arxiv.org/abs/1404.0001

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