High Order Singular Rank One Perturbations of a Positive Operator

Positive Solutions to Second Order Singular Differential Equations Involving the One-dimensional M-laplace Operator

We consider a class of second order quasilinear differential equations with singular ninlinearities. Our main purpose is to investigate in detail the asymptotic behavior of their solutions defined on a positive half-line. The set of all possible positive solutions is classified into five types according to their asymptotic behavior near infinity, and sharp conditions are established for the exi...

Rank one perturbations of self-adjoint operators

Parameter-Dependent Rank-One Perturbations of Singular Hermitian Or Symmetric Pencils

Structure-preserving generic low-rank perturbations are studied for classes of structured matrix pencils, including real symmetric, complex symmetric, and complex Hermitian pencils. For singular pencils it is analyzed which characteristic quantities stay invariant in the perturbed canonical form, and it is shown that the regular part of a structured matrix pencil is not affected by generic pert...

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...