Inverse spectral problems for Dirac operators on a star graph with mixed boundary conditions

Abstract

This paper is devoted to some inverse spectral problems for Dirac operators on a star graph with mixed boundary conditions in boundary vertices. By making use of Rouché's theorem, we derive the eigenvalue asymptotics of these operators. Besides, we show that for each of these operators, if the potentials are known a priori for all but one edge on the graph, then the potential on the remaining edge is uniquely determined by part of the potential on this edge and part of its spectrum. Our method relies upon some estimates of infinite products given by Horváth.