TY - JOUR
T1 - Spectral averaging, perturbation of singular spectra, and localization
AU - Combes, J. M.
AU - Hislop, P. D.
AU - Mourre, E.
PY - 1996
Y1 - 1996
N2 - A spectral averaging theorem is proved for one-parameter families of self-adjoint operators using the method of differential inequalities. This theorem is used to establish the absolute continuity of the averaged spectral measure with respect to Lebesgue measure. This is an important step in controlling the singular continuous spectrum of the family for almost all values of the parameter. The main application is to the problem of localization for certain families of random Schrödinger operators. Localization for a family of random Schrödinger operators is established employing these results and a multi-scale analysis.
AB - A spectral averaging theorem is proved for one-parameter families of self-adjoint operators using the method of differential inequalities. This theorem is used to establish the absolute continuity of the averaged spectral measure with respect to Lebesgue measure. This is an important step in controlling the singular continuous spectrum of the family for almost all values of the parameter. The main application is to the problem of localization for certain families of random Schrödinger operators. Localization for a family of random Schrödinger operators is established employing these results and a multi-scale analysis.
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U2 - 10.1090/s0002-9947-96-01579-6
DO - 10.1090/s0002-9947-96-01579-6
M3 - Article
AN - SCOPUS:21444432939
SN - 0002-9947
VL - 348
SP - 4883
EP - 4894
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 12
ER -