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         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2f47f251990b9280b3f0ddddf1ed72328/elkepeter",         
         "tags" : [
            "iadm","Kennedy","Laplacians","Lang","quantum","graph"
         ],
         
         "intraHash" : "f47f251990b9280b3f0ddddf1ed72328",
         "interHash" : "002810b89f26ce8985d6810f83206ff3",
         "label" : "On the eigenvalues of quantum graph Laplacians with large complex δ couplings.",
         "user" : "elkepeter",
         "description" : "",
         "date" : "2021-10-08 19:32:58",
         "changeDate" : "2021-10-13 11:54:00",
         "count" : 2,
         "pub-type": "article",
         "journal": "Portugaliae Mathematica. A Journal of the Portuguese Mathematical Society",
         "year": "2020", 
         "url": "", 
         
         "author": [ 
            "James B. Kennedy","Robin Lang"
         ],
         "authors": [
         	
            	{"first" : "James B.",	"last" : "Kennedy"},
            	{"first" : "Robin",	"last" : "Lang"}
         ],
         "volume": "77","number": "2","pages": "133-161","abstract": "\"The authors study eigenvalues of the Laplacian (the negative second derivative operator) of a compact metric graph equipped with complex δ-vertex conditions. More precisely:\r\n(a) a continuity condition is imposed at each vertex;\r\n(b) on a selected set of vertices R, the vertex conditions\r\n∑e∼vj∂∂νf|e(vj)+αjf(vj)=0\r\nare imposed, where the interaction strengths αj are complex parameters and the derivative is taken in the direction towards the vertex; and\r\n(c) on the vertices in ∖R, Kirchhoff vertex conditions are imposed.\r\n\r\n   The main focus in this article is on the asymptotic behavior of the (purely discrete) spectrum as certain coefficients αj tend to ∞ in the complex plane. If m of these coefficients tend to infinity within some sector in the open left half-plane while the remaining coefficients tend to infinity in a way such that Reαj remains bounded from below, then the authors show that exactly m eigenvalues diverge away from the positive real semi-axis. Moreover, they provide the asymptotics of these eigenvalues; the leading term is quadratic in the αj, with a coefficient depending on the vertex degrees. \r\n   As variational principles are not available for the study of such non-self-adjoint problems, the authors use a Birman-Schwinger type characterization of eigenvalues in terms of a parameter-dependent Dirichlet-to-Neumann matrix (or Titchmarsh-Weyl function). In addition, they also obtain estimates for the numerical range and the eigenvalues.\"",
         "language" : "English",
         
         "bibtexKey": "kennedy2020eigenvalues"

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         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/24ffea2310033ddac3ec52d77b210ba8a/elkepeter",         
         "tags" : [
            "iadm","graphs","Lang","quantum","Robin","Laplacian"
         ],
         
         "intraHash" : "4ffea2310033ddac3ec52d77b210ba8a",
         "interHash" : "1d9d3866bfc31d5f2d0217f6177e7cc4",
         "label" : "On the eigenvalues of the non-self-adjoint Robin Laplacian on bounded domains and compact quantum graphs.",
         "user" : "elkepeter",
         "description" : "",
         "date" : "2021-10-08 19:15:23",
         "changeDate" : "2021-10-13 11:54:00",
         "count" : 3,
         "pub-type": "phdthesis",
         "address":"Stuttgart",
         "year": "2021", 
         "url": "", 
         
         "author": [ 
            "Robin Lang"
         ],
         "authors": [
         	
            	{"first" : "Robin",	"last" : "Lang"}
         ],
         
         "supervisorgnd" : "1095129147",
         
         "language" : "English",
         
         "eventdate" : "2020-12-01",
         
         "supervisor" : "Weidl, Timo",
         
         "doi" : "10.18419/opus-11428",
         
         "bibtexKey": "lang2021eigenvalues"

      }
	  
   ]
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