Dirac–Krein Systems on Star Graphs

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dc.contributor.authorAdamyan, Vadym M.
dc.contributor.authorLanger, H.
dc.contributor.authorTretter, C.
dc.contributor.authorWinklmeier, M.
dc.contributor.authorАдамян, Вадим Мовсесовичuk
dc.date.accessioned2017-10-18T07:02:21Z
dc.date.available2017-10-18T07:02:21Z
dc.date.issued2016-08-26
dc.description.abstractWe 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.uk
dc.identifier.citationIntegral Equations and Operator Theoryuk
dc.identifier.urihttps://dspace.onu.edu.ua/handle/123456789/11062
dc.language.isoukuk
dc.relation.ispartofseries;Vol. 86, Issue 1
dc.subjectDirac operatoruk
dc.subjectDirac–Krein systemuk
dc.subjectstar graphuk
dc.subjectKrein’s resolventuk
dc.subjectformulauk
dc.subjecttrace formulauk
dc.subjectdislocation indexuk
dc.titleDirac–Krein Systems on Star Graphsuk
dc.typeArticleuk
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