We discuss rank one perturbations A_α = A + α(φ,·)φ, α ∈R , A ≥ 0 self-adjoint. Let dμα(x) be the spectral measure defined by (φ, (A_α - z)^(−1) φ) = ∫ dμ_α(x)/(x - z). We prove there is a measure dρ_∞ which is the weak limit of (1 + α^2) dμ_α(x) as α → ∞. If φ is cyclic for A, then A_∞, the strong resolvent limit of A_α, is unitarily equivalent to multiplication by x on L^2(R, dρ_∞). This generalizes results known for boundary condition dependence of Sturm-Liouville operators on half-lines to the abstract rank one case
AbstractRate of convergence theorems are proven for eigenvalues and eigenvectors of an operator form...
Let A be a selfadjoint operator in a Hilbert space h with inner product [·,·]. The rank one perturba...
Schrödinger operators on the half line. More precisely, the perturbations we consider satisfy a gene...
We discuss rank one perturbations A_α = A + α(φ,·)φ, α ∈R , A ≥ 0 self-adjoint. Let dμα(x) be the sp...
AbstractWe discuss rank one perturbations Aα = A + α(φ,·)φ, α ∈R , A ≥ 0 self-adjoint. Let dμα(x) be...
We consider a positive self-adjoint operator A and formal rank one perturbations B = A + α(φ, ·)φ, w...
Let A be a selfadjoint operator in a Hilbert space h. Its rank one perturbations A+τ(·,ω)ω, τ ∈ R, a...
Let A be a selfadjoint operator in a Hilbert space h. Its rank one perturbations A+τ(·,ω)ω, τ ∈ R, a...
AbstractWe consider rank one perturbations Aα=A+α(⋅,φ)φ of a self-adjoint operator A with cyclic vec...
Let A be a selfadjoint operator in a Hilbert space-9. Its rank one perturbations A + r(., co)co, T E...
We consider examples A_ λ = A + λ(ϕ, •)ϕ of rank one perturbations with ϕ a cyclic vector for A. We...
This dissertation details the development of several analytic tools that are used to apply the techn...
Singular finite rank perturbations of an unbounded self-adjoint operator A0 in a Hilbert space h0 ar...
Singular finite rank perturbations of an unbounded self-adjoint operator A0 in a Hilbert space h0 ar...
Given two selfadjoint operators A and V=V_+-V_-, we study the motion of the eigenvalues of the opera...
AbstractRate of convergence theorems are proven for eigenvalues and eigenvectors of an operator form...
Let A be a selfadjoint operator in a Hilbert space h with inner product [·,·]. The rank one perturba...
Schrödinger operators on the half line. More precisely, the perturbations we consider satisfy a gene...
We discuss rank one perturbations A_α = A + α(φ,·)φ, α ∈R , A ≥ 0 self-adjoint. Let dμα(x) be the sp...
AbstractWe discuss rank one perturbations Aα = A + α(φ,·)φ, α ∈R , A ≥ 0 self-adjoint. Let dμα(x) be...
We consider a positive self-adjoint operator A and formal rank one perturbations B = A + α(φ, ·)φ, w...
Let A be a selfadjoint operator in a Hilbert space h. Its rank one perturbations A+τ(·,ω)ω, τ ∈ R, a...
Let A be a selfadjoint operator in a Hilbert space h. Its rank one perturbations A+τ(·,ω)ω, τ ∈ R, a...
AbstractWe consider rank one perturbations Aα=A+α(⋅,φ)φ of a self-adjoint operator A with cyclic vec...
Let A be a selfadjoint operator in a Hilbert space-9. Its rank one perturbations A + r(., co)co, T E...
We consider examples A_ λ = A + λ(ϕ, •)ϕ of rank one perturbations with ϕ a cyclic vector for A. We...
This dissertation details the development of several analytic tools that are used to apply the techn...
Singular finite rank perturbations of an unbounded self-adjoint operator A0 in a Hilbert space h0 ar...
Singular finite rank perturbations of an unbounded self-adjoint operator A0 in a Hilbert space h0 ar...
Given two selfadjoint operators A and V=V_+-V_-, we study the motion of the eigenvalues of the opera...
AbstractRate of convergence theorems are proven for eigenvalues and eigenvectors of an operator form...
Let A be a selfadjoint operator in a Hilbert space h with inner product [·,·]. The rank one perturba...
Schrödinger operators on the half line. More precisely, the perturbations we consider satisfy a gene...