TY - JOUR
T1 - Simplicity of singular spectrum in anderson-type hamiltonians
AU - Jakšić, Vojkan
AU - Last, Yoram
PY - 2006/5/15
Y1 - 2006/5/15
N2 - We study self-adjoint operators of the form Hω = H 0 + ∑ ω(n)(δn|·) δn, where the δn's are a family of orthonormal vectors and the ω(n)'s are independent random variables with absolutely continuous probability distributions. We prove a general structural theorem that provides in this setting a natural decomposition of the Hilbert space as a direct sum of mutually orthogonal closed subspaces, which are a.s. invariant under Hω, and that is helpful for the spectral analysis of such operators. We then use this decomposition to prove that the singular spectrum of Hω is a.s. simple.
AB - We study self-adjoint operators of the form Hω = H 0 + ∑ ω(n)(δn|·) δn, where the δn's are a family of orthonormal vectors and the ω(n)'s are independent random variables with absolutely continuous probability distributions. We prove a general structural theorem that provides in this setting a natural decomposition of the Hilbert space as a direct sum of mutually orthogonal closed subspaces, which are a.s. invariant under Hω, and that is helpful for the spectral analysis of such operators. We then use this decomposition to prove that the singular spectrum of Hω is a.s. simple.
UR - http://www.scopus.com/inward/record.url?scp=33744820326&partnerID=8YFLogxK
U2 - 10.1215/S0012-7094-06-13316-1
DO - 10.1215/S0012-7094-06-13316-1
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AN - SCOPUS:33744820326
SN - 0012-7094
VL - 133
SP - 185
EP - 204
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 1
ER -