Rank-one perturbations of diagonal operators

Rank one perturbations of self-adjoint operators

Invariant Subspaces for Certain Finite-rank Perturbations of Diagonal Operators

Suppose that {ek} is an orthonormal basis for a separable, infinite-dimensional Hilbert space H. Let D be a diagonal operator with respect to the orthonormal basis {ek}. That is, D = ∑∞ k=1 λkek⊗ek, where {λk} is a bounded sequence of complex numbers. Let T = D + u1 ⊗ v1 + · · ·+ un ⊗ vn. Improving a result [2] of Foias et al., we show that if the vectors u1, . . . , un and v1, . . . , vn satis...

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.

Rank One Perturbations with Infinitesimal Coupling

We consider a positive self-adjoint operator A and formal rank one pertubrations

Bounded Rank-one Perturbations in Sampling Theory

Sampling theory concerns the problem of reconstruction of functions from the knowledge of their values at some discrete set of points. In this paper we derive an orthogonal sampling theory and associated Lagrange interpolation formulae from a family of bounded rank-one perturbations of a self-adjoint operator that has only discrete spectrum of multiplicity one. Mathematics Subject Classificatio...