Dual pair of eigenvalues in rank one singular nonsymmetric perturbations
Journal Title: Математичні Студії - Year 2017, Vol 48, Issue 2
Abstract
In the separable Hilbert space, we discuss the eigenvalue problem for a rank one singular nonselfadjoint perturbation of a selfadjoint operator A, by nonsymmetric potential (δ1≠δ2) in the form A~=A+α⟨⋅,δ1⟩δ2. We give the constructive description of such sort operator A~ which possess two new points in the point spectrum in case of weakly singular perturbations.
Authors and Affiliations
Tetyana Vdovenko, M. E. Dudkin
Keywords
Related Articles
- EP ID EP302527
- DOI 10.15330/ms.48.2.156-164
- Views 81
- Downloads 0
New generalizations of Sierpinski theorem(in Ukrainian)
We introduce the notion of equi-feeblycontinuity which ressembles S. Kempisty's equi-quasicontinuity. Using this fresh notion and weak horizontal quasicontinuity, we obtain new generalizations of Sierpinski theorem on se...
On the growth of Laplace-Stieltjes integrals
In the paper it is investigated the growth of characteristics of Laplace-Stieltjes integrals I(σ)=∫+∞0f(x)dF(x), where F is a nonnegative nondecreasing unbounded function continuous on the right on [0,+∞) and f is a nonn...
Frechet distance between weighted rooted trees
The aim of this note is to extend the notion of Frechet distance over the set of weighted rooted trees. The weighted trees naturally appear as skeletons of planar domains. The defined distance allows for defining a dista...
Progress in the open problems in theory of functions of bounded index
We give overview of solved problems in theory of functions of bounded index from the paper Bandura, A.I., Skaskiv, O.B.: Open problems for entire functions of bounded index in direction. Mat. Stud. 43(1), 103–109 (2015)....
Rings whose elements are sums or minus sums of three commuting idempotents
We completely determine up to isomorphism those rings whose elements x have the specific property that x or -x is a sum of three commuting idempotents. This statement strengthens well-known results in the subject due to...