Absolutely continuous spectrum of one random elliptic operator
type: Item
instance of: scholarly article
title: Absolutely continuous spectrum of one random elliptic operator
zbMATH Open document ID: 1154.47040
author: B. E. Eshmatov
published in: Journal of Functional Analysis
publication date: 2008-09-01T00:00:00Z
review text: This paper concerns the differential operator \(H_0=-\Delta +\tau \xi(x)| x| ^{-\varepsilon}(-\Delta_\theta)\), perturbed by a random potential \(V\) (the same as that in Anderson's model). Here, \(\varepsilon>0\), \(\tau>0\), \(\Delta_\theta\) is the Laplace--Beltrami operator on the unit sphere, and \(\xi\) the characteristic function of the unit ball. The author proves that the operator \(H_0\pm V\) has absolutely continuous spectrum all over the positive half-line \([0,\infty)\), if the dimension \(d\geq 5\) and \(\varepsilon<2/(d+1)\).
reviewed by: Ti-Jun Xiao
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 47B80
Mathematics Subject Classification ID: 35P05
zbMATH DE Number: 5318666
zbMATH Keywords: absolutely continuous spectrum
zbMATH Keywords: random operators
zbMATH Keywords: trace formulas
MaRDI profile type: Publication
full work available at URL: j.jfa.2008.04.019
OpenAlex ID: W2019697260
cites work: Q4654524
cites work: On random Schrödinger operators on \(\mathbb{Z}^2\)
cites work: Q4424442
cites work: Maximum Properties and Inequalities for the Eigenvalues of Completely Continuous Operators
cites work: Absolutely continuous spectrum of Schrödinger operators with slowly decaying and oscillating potentials
cites work: Q3889819
cites work: Q4110023
DOI: 10.1016/J.JFA.2008.04.019
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description: scientific article; zbMATH DE number 5318666