Inverse eigenvalue problem for a simple star graph
William Rundell
Texas A&M University, College Station, United StatesPaul Sacks
Iowa State University, Ames, USA
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Abstract
A Schrödinger operator and associated spectra may be defined for a graph by identifying edges with intervals of , on which coefficient functions are defined, imposing appropriate matching conditions at the internal vertices and boundary conditions at the external vertices. Following earlier work of Pivovarchik [14], we consider an inverse eigenvalue problem for a graph consisting of three equal length edges meeting at a single point, where the spectral data is the Dirichlet eigenvalues of the graph together with the Dirichlet spectra of the three individual edges. We derive, discuss and demonstrate a constructive solution method, obtain an alternative uniqueness proof, and discuss several kinds of generalizations.
Cite this article
William Rundell, Paul Sacks, Inverse eigenvalue problem for a simple star graph. J. Spectr. Theory 5 (2015), no. 2, pp. 363–380
DOI 10.4171/JST/101