کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4590925 1334995 2011 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Preservation of a.c. spectrum for random decaying perturbations of square-summable high-order variation
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Preservation of a.c. spectrum for random decaying perturbations of square-summable high-order variation
چکیده انگلیسی

We consider random self-adjoint Jacobi matrices of the form(Jωu)(n)=an(ω)u(n+1)+bn(ω)u(n)+an−1(ω)u(n−1)(Jωu)(n)=an(ω)u(n+1)+bn(ω)u(n)+an−1(ω)u(n−1) on ℓ2(N)ℓ2(N), where {an(ω)>0}{an(ω)>0} and {bn(ω)∈R}{bn(ω)∈R} are sequences of random variables on a probability space (Ω,dP(ω))(Ω,dP(ω)) such that there exists q∈Nq∈N, such that for any l∈Nl∈N,β2l(ω)=al(ω)−al+q(ω)andβ2l+1(ω)=bl(ω)−bl+q(ω) are independent random variables of zero mean satisfying∑n=1∞∫Ωβn2(ω)dP(ω)<∞. Let JpJp be the deterministic periodic (of period q  ) Jacobi matrix whose coefficients are the mean values of the corresponding entries in JωJω. We prove that for a.e. ω  , the a.c. spectrum of the operator JωJω equals to and fills the spectrum of JpJp. If, moreover,∑n=1∞∫Ωβn4(ω)dP(ω)<∞, then for a.e. ω  , the spectrum of JωJω is purely absolutely continuous on the interior of the bands that make up the spectrum of JpJp.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 260, Issue 4, 28 February 2011, Pages 1029–1044
نویسندگان
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