An Inverse Spectral Problem for the Sturm-Liouville Operator on a Three-Star Graph. (27th May 2012)

• Record Type: Journal Article
• Authors: Dehghani Tazehkand, I.; Jodayree Akbarfam, A.
• Other Names: Georges D. Academic Editor.
• Is Part Of: ISRN applied mathematics. Volume 2012(2012)
• Publication Date: 2012-05-27
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; Electronic journals; 510
• DOI: 10.5402/2012/132842
• Languages: English
• ISSNs: 2090-5564

Abstract

Abstract : We study an inverse spectral problem for the Sturm-Liouville operator on a three-star graph with the Dirichlet and Robin boundary conditions in the boundary vertices and matching conditions in the internal vertex. As spectral characteristics, we consider the spectrum of the main problem together with the spectra of two Dirichlet-Dirichlet problems and one Robin-Dirichlet problem on the edges of the graph and investigate their properties and asymptotic behavior. We prove that if these four spectra do not intersect, then the inverse problem of recovering the operator is uniquely solvable. We give an algorithm for the solution of the inverse problem with respect to this quadruple of spectra.