| Post: Convergence of resonances on thin branched quantum wave guides (2008) | |||||||||||||||
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| Abstract. We prove an abstract criterion stating resolvent convergence in the case of operators acting in different Hilbert spaces. This result is then applied to the case of Laplacians on a family Xε of branched quantum waveguides. Combining it with an exterior complex scaling we show, in particular, that the resonances on Xε approximate those of the Laplacian with “free ” boundary conditions on X0, the skeleton graph of Xε. 1. | |||||||||||||||
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