Kato's inequality and asymptotic spectral properties for discrete magnetic Laplacians

Details Kato's inequality and asymptotic spectral properties for discrete magnetic Laplacians Kato's inequality and asymptotic spectral properties for discrete magnetic Laplacians

2003-12-24

arxiv.org/abs/math/0312450v3

Contemporary Mathematics, vol. 398 (2006) 69-81.

Mathematics

Spectral Theory

14 pages, latex2e, final version, to appear in "Contemporary Math."

Scientific paper

In this paper, a discrete form of the Kato inequality for discrete magnetic Laplacians on graphs is used to study asymptotic properties of the spectrum of discrete magnetic Schrodinger operators. We use the existence of a ground state with suitable properties for the ordinary combinatorial Laplacian and semigroup domination to relate the combinatorial Laplacian with the discrete magnetic Laplacian.

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