Trace formulae for Schrödinger operators on metric graphs with applications to recovering matching conditions - Kiselev, A. V.; Ershova, Yu. (Methods of Functional Analysis and Topology, 2014)
The paper is a continuation of the study started in [8]. Schrödinger 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.