Trace formulae for Schrödinger operators on metric graphs with applications to recovering matching conditions. (English) Zbl 1313.34093
The paper is a continuation of the authors [Methods Funct. Anal. Topol. 18, No. 4, 343–359 (2012; Zbl 1289.34088)]. The authors consider Schrödinger operators on finite compact metric graphs with matching conditions of \(\delta\) type at the graph vertices. It is assumed that the graphs do not contain loops. Using an appropriate boundary triplet, the authors study the asymptotic behavior of the Weyl function. This enables them to obtain a trace formula for a pair of Schrödinger operators on the same metric graph, which results in a uniqueness theorem for an inverse problem of restoring the matching conditions from the spectrum.
Reviewer: Anatoly N. Kochubei (Kyïv)
MSC:
| 34B45 | Boundary value problems on graphs and networks for ordinary differential equations |
| 47E05 | General theory of ordinary differential operators |
| 34A55 | Inverse problems involving ordinary differential equations |
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
| 34B20 | Weyl theory and its generalizations for ordinary differential equations |
| 34E05 | Asymptotic expansions of solutions to ordinary differential equations |
