Spectral data characterization for the Sturm-Liouville operator on the star-shaped graph (Q2220131)

The inverse spectral problem is studied for the matrix Sturm-Liouville equation \[ -Y''(x)+Q(x)Y(x)=\lambda Y(x),\; x\in(0,\pi) \] with separated boundary conditions; here \(Q(x)\) is a diagonal \(m\times m\) matrix. Necessary and sufficient conditions for the solvability of the inverse problem are obtained by the method of spectral mappings. As a corollary, similar results are obtained for the Sturm-Liouville operator on a star-shaped graph.