Spectral analysis of metric graphs and related spaces

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dc.creatorPost, Olaf
dc.date2007-12-10
dc.date2008-02-15
dc.date.accessioned2026-07-07T09:20:41Z
dc.date.available2026-07-07T09:20:41Z
dc.descriptionThe aim of the present article is to give an overview of spectral theory on metric graphs guided by spectral geometry on discrete graphs and manifolds. We present the basic concept of metric graphs and natural Laplacians acting on it and explicitly allow infinite graphs. Motivated by the general form of a Laplacian on a metric graph, we define a new type of combinatorial Laplacian. With this generalised discrete Laplacian, it is possible to relate the spectral theory on discrete and metric graphs. Moreover, we describe a connection of metric graphs with manifolds. Finally, we comment on Cheeger's inequality and trace formulas for metric and discrete (generalised) Laplacians.
dc.description24 pages, extended version of a lecture held at the EPF Lausanne, some references added and typos corrected
dc.identifierhttps://arxiv.org/abs/0712.1507
dc.identifierhttp://arxiv.org/abs/0712.1507
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154800
dc.subjectCombinatorics
dc.subjectMathematical Physics
dc.subjectDifferential Geometry
dc.titleSpectral analysis of metric graphs and related spaces
dc.typetext

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