%0 Journal Article
%T Trace formulae for Schrodinger operators on metric graphs with applications to recovering matching conditions
%A Yulia Ershova
%A Alexander V. Kiselev
%J Mathematics
%D 2014
%I arXiv
%X 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 $\delta$ 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.
%U http://arxiv.org/abs/1404.0001v1