Adamyan, Vadym M.Langer, H.Tretter, C.Winklmeier, M.Адамян, Вадим Мовсесович2017-10-182017-10-182016-08-26Integral Equations and Operator Theoryhttps://dspace.onu.edu.ua/handle/123456789/11062We 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.ukDirac operatorDirac–Krein systemstar graphKrein’s resolventformulatrace formuladislocation indexArticle