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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.

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

Citations:

Zbl 1289.34088
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