Abstract

In this work, an inverse spectral problem is studied for the Sturm–Liouville differential operator on a d-star graph. Using a new type of spectral data, involving a fraction of the eigenvalues and knowledge of potential over a corresponding fraction of the interval, we prove that the partial information both in the spectrum and the potential determines the potential completely. This extends the results of the previous work of the first author (J. Math. Anal. Appl. 365, 2010, 742–749). The proofs in this work rely on the properties of analytic functions, and so differ from those in the mentioned article.