Hardy inequality and asymptotic eigenvalue distribution for discrete Laplacians

Sylvain Golenia (1)

1 IMB - Institut de Mathématiques de Bordeaux

In this paper we study in detail some spectral properties of the magnetic discrete Laplacian. We identify its form-domain, characterize the absence of essential spectrum and provide the asymptotic eigenvalue distribution.

Mots clés: magnetic discrete Laplacian; locally finite graphs; self-adjointness; unboundedness; semi-boundedness; spectrum; spectral graph theory; asympotic of eigenvalues; essential spectrum

Domaines: Théorie spectrale [math.SP]; Analyse fonctionnelle [math.FA]

Sylvain Golenia. Hardy inequality and asymptotic eigenvalue distribution for discrete Laplacians. Journal of Functional Analysis, 2014, pp.Funct. Anal. 266 (2014), no. 5, 2662-2688. ⟨hal-00598054v4⟩