Two-parametric ${\delta'}$ -interactions: approximation by Schrödinger operators with localized rank-two perturbations

Hyponormal Operators with Rank-two Self-commutators

In this paper it is shown that if T ∈ L(H) satisfies (i) T is a pure hyponormal operator; (ii) [T ∗, T ] is of rank-two; and (iii) ker [T ∗, T ] is invariant for T , then T is either a subnormal operator or the Putinar’s matricial model of rank two. More precisely, if T |ker [T∗,T ] has the rank-one self-commutator then T is subnormal and if instead T |ker [T∗,T ] has the ranktwo self-commutato...

The Delta - Wye Approximation Procedurefor Two - terminal

The Delta-Wye Approximation Procedure (DWAP) is a procedure for estimating the two-terminal reliability of an undirected planar network G = (V; E) by reducing the network to a single edge via a sequence of local graph transformations. It combines the probability equations of Lehman | whose solutions provide bounds and approximations of two-terminal reliability for the individual transformations...

Rank one perturbations of self-adjoint operators

Schrödinger Operators with Local Interactions on a Discrete Set

Spectral properties of 1-D Schrödinger operators HX,α := − d 2 dx2 + ∑ xn∈X αnδ(x − xn) with local point interactions on a discrete set X = {xn}n=1 are well studied when d∗ := infn,k∈N |xn − xk| > 0. Our paper is devoted to the case d∗ = 0. We consider HX,α in the framework of extension theory of symmetric operators by applying the technique of boundary triplets and the corresponding Weyl funct...

Solvable Two - Dimensional Schrödinger

S.P.Novikov: University of Maryland at College Park, Department of Mathematics and IPST, College Park MD 20742-2431 USA and Landau Institute for Theoretical Physics, Moscow 117940, Kosygin street 2, Russia. E-mail adress [email protected] A.P.Veselov: Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK and Department of Mathematics and Mec...