Eigenvalue asymptotics for Schrödinger operators on sparse graphs
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en
Document de travail - Pré-publication
Resumen en inglés
We consider Schrödinger operators on sparse graphs. The geometric definition of sparseness turn out to be equivalent to a functional inequality for the Laplacian. In consequence, sparseness has in turn strong spectral and ...Leer más >
We consider Schrödinger operators on sparse graphs. The geometric definition of sparseness turn out to be equivalent to a functional inequality for the Laplacian. In consequence, sparseness has in turn strong spectral and functional analytic consequences. Specifically, one consequence is that it allows to completely describe the form domain. Moreover, as another consequence it leads to a characterization for discreteness of the spectrum. In this case we determine the first order of the corresponding eigenvalue asymptotics.< Leer menos
Palabras clave en inglés
discrete laplacian
eigenvalues
asymptotic
planarity
sparse
functional inequality
Orígen
Importado de HalCentros de investigación