Eigenvalue asymptotics for Schrödinger operators on sparse graphs
Language
en
Document de travail - Pré-publication
English Abstract
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 ...Read more >
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.Read less <
English Keywords
discrete laplacian
eigenvalues
asymptotic
planarity
sparse
functional inequality
Origin
Hal imported