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The first aim of this monograph is to introduce into the asymptotic analysis of graphlike spaces (also called graph-like manifolds, tubular branched manifolds, graph neighbourhoods, fat graphs, network-shaped domains, inflated or d-dimensional graphs) in the 0-thickness limit and the convergence of associated operators and related objects. The second aim is to provide necessary tools from functional analysis and operator theory to treat such convergence problems, where operators act in different spaces, and where spaces are coupled according to a graph.
KeywordsHeat Kernel Essential Spectrum Quantum Graph Vertex Neighbourhood Complex Dilation
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