A. K. Motovilov

activity

19952024

most citedBinding Energies and Scattering Observables in the 4^He_3 Atomic System

74 citations · 645 across the 66 of their papers we have counts for

collaborators

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23 papers · 1 filter

math.SP2018★ 2 cited

Preserving of the unconditional basis property under non-self-adjoint perturbations of self-adjoint operators

Alexander K. Motovilov, Andrei A. Shkalikov

Let $T$ be a self-adjoint operator in a Hilbert space $H$ with domain $D (T)$ . Assume that the spectrum of $T$ is confined in the union of disjoint intervals $Δ_k =[α_{2k-1…

math.SP2017★ 1 cited

Solvability of the operator Riccati equation in the Feshbach case

Sergio Albeverio, Alexander K. Motovilov

We consider a bounded block operator matrix of the form $L = (A C B D),$ where the main-diagonal entries $A$ and $D$ are self-adj…

math.SP2017★ 2 cited

Unconditional bases of subspaces related to non-self-adjoint perturbations of self-adjoint operators

A. K. Motovilov, A. A. Shkalikov

Assume that $T$ is a self-adjoint operator on a Hilbert space $H$ and that the spectrum of $T$ is confined in the union $⋃_{j \in J} Δ_{j}$ , $J \subseteq Z$ , of…

math.SP2016★ 4 cited

On invariant graph subspaces of a J-self-adjoint operator in the Feshbach case

Sergio Albeverio, Alexander K. Motovilov

We consider a J-self-adjoint 2x2 block operator matrix L in the Feshbach spectral case, that is, in the case where the spectrum of one main-diagonal entry is embedded into the abso…

math.SP2012

Comment on `The tan θ theorem with relaxed conditions', by Y. Nakatsukasa

Alexander K. Motovilov

We show that in case of the spectral norm, one of the main results of the recent paper "The tan θ theorem with relaxed conditions", by Yuji Nakatsukasa, published in Linear Algebra…

math.SP2011★ 14 cited

Sharpening the norm bound in the subspace perturbation theory

Sergio Albeverio, Alexander K. Motovilov

Let A be a self-adjoint operator on a Hilbert space H. Assume that σ is an isolated component of the spectrum of A, i.e. dist(σ,Σ)=d>0 where Σ=spec(A)\σ. Suppose that V is a bounde…

math.SP2010★ 7 cited

The a priori Tan Theta Theorem for spectral subspaces

Sergio Albeverio, Alexander K. Motovilov

Let A be a self-adjoint operator on a separable Hilbert space H. Assume that the spectrum of A consists of two disjoint components s_0 and s_1 such that the set s_0 lies in a finit…

math.SP2009★ 16 cited

Bounds on the spectrum and reducing subspaces of a J-self-adjoint operator

Sergio Albeverio, Alexander K. Motovilov, Christiane Tretter

Given a self-adjoint involution J on a Hilbert space H, we consider a J-self-adjoint operator L=A+V on H where A is a possibly unbounded self-adjoint operator commuting with J and…

math.SP2008★ 32 cited

Bounds on variation of spectral subspaces under J-self-adjoint perturbations

S. Albeverio, A. K. Motovilov, A. A. Shkalikov

Let $A$ be a self-adjoint operator on a Hilbert space $\fH$. Assume that the spectrum of $A$ consists of two disjoint components $σ_{0}$ and $σ_{1}$ . Let $V$ be a bounded operator on $…

math.SP2005

The a priori tanθtheorem for eigenvectors

Sergio Albeverio, Alexander K. Motovilov, Alexei V. Selin

Let $A$ be a self-adjoint operator on a Hilbert space $\fH$. Assume that the spectrum of $A$ consists of two disjoint components $σ_{0}$ and $σ_{1}$ such that the convex hull of the se…

math.SP2004★ 10 cited

Operator integrals with respect to a spectral measure and solutions to some operator equations

Sergio Albeverio, Alexander K. Motovilov

We introduce the concept of Stieltjes integral of an operator-valued function with respect to the spectral measure associated with a normal operator. We give sufficient conditions…

math.SP2004★ 12 cited

Some sharp norm estimates in the subspace perturbation problem

Alexander K. Motovilov, Alexei V. Selin

We discuss the spectral subspace perturbation problem for a self-adjoint operator. Assuming that the convex hull of a part of its spectrum does not intersect the remainder of the s…

math.SP2003★ 29 cited

Perturbation of spectra and spectral subspaces

Vadim Kostrykin, Konstantin A. Makarov, Alexander K. Motovilov

We consider the problem of variation of spectral subspaces for linear self-adjoint operators under off-diagonal perturbations. We prove a number of new optimal results on the shift…

math.SP2003

A generalization of the $t an 2Θ$ Theorem

Vadim Kostrykin, Konstantin A. Makarov, Alexander K. Motovilov

Let $A$ be a bounded self-adjoint operator on a separable Hilbert space $H$ and $H_{0} \subset H$ a closed invariant subspace of $A$ .…

math.SP2002★ 30 cited

On the existence of solutions to the operator Riccati equation and the tanΘtheorem

Vadim Kostrykin, Konstantin A. Makarov, Alexander K. Motovilov

Let A and C be self-adjoint operators such that the spectrum of A lies in a gap of the spectrum of C and let d>0 be the distance between the spectra of A and C. We prove that under…

math.SP2002

Existence and uniqueness of solutions to the operator Riccati equation. A geometric approach

Vadim Kostrykin, Konstantin A. Makarov, Alexander K. Motovilov

We introduce a new concept of unbounded solutions to the operator Riccati equation $A_{1} X - X A_{0} - X V X + V^{*} = 0$ and give a complete description of its solutions associated…

math.SP2002★ 26 cited

On a Subspace Perturbation Problem

Vadim Kostrykin, Konstantin A. Makarov, Alexander K. Motovilov

We discuss the problem of perturbation of spectral subspaces for linear self-adjoint operators on a separable Hilbert space. Let $A$ and $V$ be bounded self-adjoint operators. Assu…

math.SP2001

Factorization Theorem for the Transfer Function Associated with an Unbounded Non-Self-Adjoint 2x2 Operator Matrix

V. Hardt, R. Mennicken, A. K. Motovilov

We construct operators which factorize the transfer function associated with a non-self-adjoint 2x2 operator matrix whose diagonal entries can have overlapping spectra and whose of…

math.SP2001★ 44 cited

Graph Subspaces and the Spectral Shift Function

Sergio Albeverio, Konstantin A. Makarov, Alexander K. Motovilov

We extend the concept of Lifshits--Krein spectral shift function associated with a pair of self-adjoint operators to the case of pairs of admissible operators that are similar to s…

math.SP1999

Factorization theorem for the transfer function of a 2x2 operator matrix with unbounded couplings

V. Hardt, R. Mennicken, A. K. Motovilov

We consider the analytic continuation of the transfer function associated with a 2x2 operator matrix having unbounded couplings into unphysical sheets of its Riemann surface. We co…

math.SP1999★ 14 cited

Monotonicity and Concavity Properties of The Spectral Shift Function

F. Gesztesy, K. A. Makarov, A. K. Motovilov

Let $H_{0}$ and $V (s)$ be self-adjoint, $V, V^{'}$ continuously differentiable in trace norm with $V^{''} (s) \geq 0$ for $s \in (s_{1}, s_{2})$ , and denote by ${E_{H (s)} (λ)}_{λ \in R}$ the fami…

math.SP1998

Removal of the resolvent-like dependence on the spectral parameter from perturbations

A. K. Motovilov

The spectral problem (A + V(z))ψ=zψis considered with A, a self-adjoint operator. The perturbation V(z) is assumed to depend on the spectral parameter z as resolvent of another sel…

math.SP1998★ 3 cited

Operator interpretation of resonances generated by some operator matrices

R. Mennicken, A. K. Motovilov

We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct a family of non-s…

Preserving of the unconditional basis property under non-self-adjoint perturbations of self-adjoint operators

Solvability of the operator Riccati equation in the Feshbach case

Unconditional bases of subspaces related to non-self-adjoint perturbations of self-adjoint operators

On invariant graph subspaces of a J-self-adjoint operator in the Feshbach case

Comment on `The tan θ theorem with relaxed conditions', by Y. Nakatsukasa

Sharpening the norm bound in the subspace perturbation theory

The a priori Tan Theta Theorem for spectral subspaces

Bounds on the spectrum and reducing subspaces of a J-self-adjoint operator

Bounds on variation of spectral subspaces under J-self-adjoint perturbations

The a priori tanθtheorem for eigenvectors

Operator integrals with respect to a spectral measure and solutions to some operator equations

Some sharp norm estimates in the subspace perturbation problem

Perturbation of spectra and spectral subspaces

A generalization of the tan2Θ Theorem

On the existence of solutions to the operator Riccati equation and the tanΘtheorem

Existence and uniqueness of solutions to the operator Riccati equation. A geometric approach

On a Subspace Perturbation Problem

Factorization Theorem for the Transfer Function Associated with an Unbounded Non-Self-Adjoint 2x2 Operator Matrix

Graph Subspaces and the Spectral Shift Function

Factorization theorem for the transfer function of a 2x2 operator matrix with unbounded couplings

Monotonicity and Concavity Properties of The Spectral Shift Function

Removal of the resolvent-like dependence on the spectral parameter from perturbations

Operator interpretation of resonances generated by some operator matrices

A generalization of the $t an 2Θ$ Theorem