About: Convergence of spectra of graph-like thin manifolds

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Uvažujeme množinu kompaktních variet, jež kolabuje vzhledem ke vhodnému parametru na graf. Hlavní výsledek je, že spektrum Laplace-Beltramiho operátoru konverguje ke spektru (diferenciélniho)Laplaciánu na grafu s Kirchhoffovými hraničními podmínkami ve vrcholech. (cs) We consider a family of compact manifolds which shrinks with respect to an appropriate parameter to a graph. The main result is that the spectrum of the Laplace-Beltrami operator converges to the spectrum of the (differential) Laplacian on the graph with Kirchhoff boundary conditions at the vertices. On the other hand, if the shrinking at the vertex parts of the manifold is sufficiently slower comparing to that of the edge parts, the limiting spectrum corresponds to decoupled edges with Dirichlet boundary conditions at the endpoints. At the borderline between the two regimes we have a third possibility when the limiting spectrum can be described by a nontrivial coupling at the vertices. We consider a family of compact manifolds which shrinks with respect to an appropriate parameter to a graph. The main result is that the spectrum of the Laplace-Beltrami operator converges to the spectrum of the (differential) Laplacian on the graph with Kirchhoff boundary conditions at the vertices. On the other hand, if the shrinking at the vertex parts of the manifold is sufficiently slower comparing to that of the edge parts, the limiting spectrum corresponds to decoupled edges with Dirichlet boundary conditions at the endpoints. At the borderline between the two regimes we have a third possibility when the limiting spectrum can be described by a nontrivial coupling at the vertices. (en)
Title	Convergence of spectra of graph-like thin manifolds Konvergence spekter tenkych variet typu grafu (cs) Convergence of spectra of graph-like thin manifolds (en)
skos:prefLabel	Convergence of spectra of graph-like thin manifolds Konvergence spekter tenkych variet typu grafu (cs) Convergence of spectra of graph-like thin manifolds (en)
skos:notation	RIV/61389005:_____/05:00032293!RIV06-AV0-61389005
http://linked.open.../vavai/riv/strany	77;115
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(IAA1048101), Z(AV0Z1048901)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2006
http://linked.open...aciTvurceVysledku	Exner, Pavel
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav jaderné fyziky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	516402
http://linked.open...ai/riv/idVysledku	RIV/61389005:_____/05:00032293
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	branched quantum wave guides; convergence of eigenvalues; singular limit; Laplace-Beltrami operator (en)
http://linked.open.../riv/klicoveSlovo	singular limit Laplace-Beltrami operator branched quantum wave guides convergence of eigenvalues
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[08C0499176E1]
http://linked.open...i/riv/nazevZdroje	Journal of Geometry and Physics
http://linked.open...in/vavai/riv/obor	BE
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Quantum graphs and related systems
http://linked.open...UplatneniVysledku	2005
http://linked.open...v/svazekPeriodika	54
http://linked.open...iv/tvurceVysledku	Exner, Pavel Post, O.
http://linked.open...n/vavai/riv/zamer	Theoretical and experimental investigation of atomic nuclei and exploitation of nuclear methods in interdisciplinary research
issn	0393-0440
number of pages	39 (xsd:int)
is http://linked.open...avai/riv/vysledek of	Convergence of spectra of graph-like thin manifolds

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