Rank One Perturbations at Infinite Coupling
نویسنده
چکیده
We discuss rank one perturbationsAα = A+α(φ, ·)φ,α ∈ R , A ≥ 0 self-adjoint. Let dμα(x) be the spectral measure defined by (φ, (Aα − z)−1φ) = ∫ dμα(x)/(x− z). We prove there is a measure dρ∞ which is the weak limit of (1 + α)dμα(x) as α → ∞. If φ is cyclic for A, then A∞, the strong resolvent limit of Aα, is unitarily equivalent to multiplication by x on L(R , dρ∞). This generalizes results known for boundary condition dependence of Sturm-Liouville operators on half-lines to the abstract rank one case. §
منابع مشابه
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