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On the Inverse Spectral Problems for Quantum Graphs

  • M. OlivieriEmail author
  • D. Finco
Chapter
Part of the Springer INdAM Series book series (SINDAMS, volume 18)

Abstract

We review some aspects of inverse spectral problems for quantum graphs. Under hypothesis of rational independence of lengths of edges it is possible, thanks to trace formulas, to reconstruct information on compact and non compact graphs from the knowledge, respectively, of the spectrum of Laplacian and of the scattering phase. In the case of Sturm-Liouville operators defined on compact graphs and in general for differential operators on compact star-graphs, unknown potentials can be recovered from the knowledge of the spectrum of operators obtained imposing different boundary conditions.

Keywords

Inverse problems Inverse scattering problems Sturm-Liouville operators Quantum graphs 

MSC 2010

35R30 81U40 34B24 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversitá di Roma “La Sapienza”RomeItaly
  2. 2.Facoltá di IngegneriaUniversitá Telematica Internazionale “Uninettuno”RomeItaly

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