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Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 8
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Articles

Non-random perturbations of the Anderson Hamiltonian in the 1-D case

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Pages 1755-1765 | Received 07 May 2012, Accepted 18 May 2012, Published online: 11 Jul 2012
 

Abstract

Recently (S. Molchanov and B. Vainberg, Non-random perturbations of the Anderson Hamiltonian, J. Spectral Theory 50 (2) (2011), pp. 179–195), two of the authors applied the Lieb method to the study of the negative spectrum for particular operators of the form H = H 0 − W. Here, H 0 is the generator of the positive stochastic (or sub-stochastic) semigroup, W(x) ≥ 0 and W(x) → 0 as x → ∞ on some phase space X. They used the general results in several ‘exotic’ situations, among them the Anderson Hamiltonian H 0. In the 1-D case, the subject of this article, we will prove similar, but more precise results.

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