Adamyan, V.V.AdamyanLanger, HeinzHeinzLangerTretter, ChristianeChristianeTretterWinklmeier, MonikaMonikaWinklmeier2024-10-252024-10-252016-09https://boris-portal.unibe.ch/handle/20.500.12422/152676We study the spectrum of a self-adjoint Dirac-Krein operator with potential on a compact star graph G with a finite number n of edges. This operator is defined by a Dirac-Krein differential expression with summable matrix potentials on each edge, by self-adjoint boundary conditions at the outer vertices, and by a self-adjoint matching condition at the common central vertex of G. Special attention is paid to Robin matching conditions with parameter τ∈R∪{∞}. Choosing the decoupled operator with Dirichlet condition at the central vertex as a reference operator, we derive Krein's resolvent formula, introduce corresponding Weyl-Titchmarsh functions, study the multiplicities, dependence on τ, and interlacing properties of the eigenvalues, and prove a trace formula. Moreover, we show that, asymptotically for R→∞, the difference of the number of eigenvalues in the intervals [0,R) and [−R,0) deviates from some integer κ0, which we call dislocation index, at most by n+2.en500 - Science::510 - Mathematicsarticle10.7892/boris.997651608.05865v110.1007/s00020-016-2311-4