Traces and inverse nodal problems for Dirac-type integro-differential operators on a graph

摘要

In this paper, Dirac-type integro-differential operators on the star graph are studied. First, we derive the asymptotic expressions for the large eigenvalues. Second, the regularized trace formulae are obtained for these operators. We also provide asymptotic expressions for the nodal points and give a constructive procedure for solving an inverse nodal problem.