Rank one perturbations of self-adjoint operators
نویسندگان
چکیده
منابع مشابه
On Rank One H−3-Perturbations of Positive Self–adjoint Operators
Rank one H−3 perturbations of positive self–adjoint operators are constructed using a certain extended Hilbert space and regularization procedures. Applications to Schrödinger operators with point interactions are discussed.
متن کاملSingularly Perturbed Self-Adjoint Operators in Scales of Hilbert spaces
Finite rank perturbations of a semi-bounded self-adjoint operator A are studied in the scale of Hilbert spaces associated with A. A concept of quasi-boundary value space is used to describe self-adjoint operator realizations of regular and singular perturbations of A by the same formula. As an application the one-dimensional Schrödinger operator with generalized zero-range potential is consider...
متن کاملCyclicity in Rank-one Perturbation Problems
The property of cyclicity of a linear operator, or equivalently the property of simplicity of its spectrum, is an important spectral characteristic that appears in many problems of functional analysis and applications to mathematical physics. In this paper we study cyclicity in the context of rank-one perturbation problems for self-adjoint and unitary operators. We show that for a fixed non-zer...
متن کاملCanonical Systems and Finite Rank Perturbations of Spectra
We use Rokhlin’s Theorem on the uniqueness of canonical systems to find a new way to establish connections between Function Theory in the unit disk and rank one perturbations of self-adjoint or unitary operators. In the n-dimensional case, we prove that for any cyclic self-adjoint operator A, operator Aλ = A + Σ k=1 λk(·, φk)φk is pure point for a.e. λ = (λ1, λ2, ..., λn) ∈ R n iff operator Aη ...
متن کاملA Krein-like Formula for Singular Perturbations of Self-adjoint Operators and Applications
Given a self-adjoint operator A : D(A) ⊆ H → H and a continuous linear operator τ : D(A) → X with Range τ ′ ∩ H = {0}, X a Banach space, we explicitly construct a family A Θ of self-adjoint operators such that any A Θ coincides with the original A on the kernel of τ . Such a family is obtained by giving a Krĕın-like formula where the role of the deficiency spaces is played by the dual pair (X ,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013