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Spectral Analysis on Graph-Like Spaces
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In this monograph, we analyse thin tubular structures, so-called “graph-like spaces”, and their natural limits, when the radius of a graph-like space tends to zero. The limit space is typically a metric graph, i.e. a graph, where each edge is associated a length, and therefore, the space turns into a one-dimensional manifold with singularities at the vertices. On both, the graph-like spaces and the metric graph, we can naturally define Laplace-like differential operators. We are interested in asymptotic properties of such operators. In particular, we show norm resolvent convergence, convergence of the spectra and resonances.
Tubular structures with small radius have attracted a lot of attention in the last years. Tubular structures are frequently used in different areas such as mathematical physics to describe properties of nano-structures, in spectral geometry to provide examples with given spectral properties, or in global analysis to calculate spectral invariants.
Olaf Post - Personal Name
1st Edtion
978-3-642-23839-0
NONE
Spectral Analysis on Graph-Like Spaces
Management
English
Springer Heidelberg Dordrecht
2012
USA
1-450
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