In this talk, we consider the Laplace operator on a star-shaped graph with nonlocal integral matching condition. This operator is adjoint to the functional-differential operator with frozen argument at the central vertex of the graph. We study the inverse problem that consists in the recovery of the integral condition coefficients from the eigenvalues. The uniqueness theorem, the spectrum characterization, and two reconstruction algorithms have been obtained for this inverse problem. We will discuss the connection of our results with the study of inverse problems for functional-differential operators with frozen argument and other related issues.

This talk is based on the preprint: Bondarenko, N. P. Inverse problem for a differential operator on a star-shaped graph with nonlocal matching condition, https://arxiv.org/abs/2201.10461