511 citations · 1.7k across the 69 of their papers we have counts for
12 papers · 1 filter
Functional model for extensions of symmetric operators and applications to scattering theory
Kirill D. Cherednichenko, Alexander V. Kiselev, Luis O. Silva
On the basis of the explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equa…
Isospectrality for graph Laplacians under the change of coupling at graph vertices: necessary and sufficient conditions
Yulia Ershova, Irina I. Karpenko, Alexander V. Kiselev
Laplace operators on finite compact metric graphs are considered under the assumption that matching conditions at graph vertices are of and types. Assuming rational indepe…
Isospectrality for graph Laplacians under the change of coupling at graph vertices
Yulia Ershova, Irina I. Karpenko, Alexander V. Kiselev
Laplacian operators on finite compact metric graphs are considered under the assumption that matching conditions at graph vertices are of and types. An infinite series of…
On Cayley Identity for Self-Adjoint Operators in Hilbert Spaces
Alexander V. Kiselev, Serguei Naboko
We prove an analogue to the Cayley identity for an arbitrary self-adjoint operator in a Hilbert space. We also provide two new ways to characterize vectors belonging to the singula…
Spectral Properties of Schrödinger Operators with Decaying Potentials
Sergey A. Denisov, Alexander Kiselev
We review recent advances in the spectral theory of Schrödinger operators with decaying potentials. The area has seen spectacular progress in the past few years, stimulated by seve…
Dynamical upper bounds on wavepacket spreading
R. Killip, A. Kiselev, Y. Last
We derive a general upper bound on the spreading rate of wavepackets in the framework of Schrödinger time evolution. Our result consists of showing that a portion of the wavepacket…
Absolutely continuous spectrum of Stark operators
M. Christ, A. Kiselev
We prove several new results on the absolutely continuous spectra of perturbed one-dimensional Stark operators. First, we find new classes of perturbations, characterized mainly by…
Scattering and wave operators for one-dimensional Schrödinger operators with slowly decaying nonsmooth potentials
M. Christ, A. Kiselev
We prove existence of modified wave operators for one-dimensional Schrödinger equations with potential in , . If in addition the potential is conditionally integr…
Solutions, Spectrum, and Dynamica for Schrödinger Operators on Infinite Domains
Alexander Kiselev, Yoram Last
Let H be a Schrödinger operator defined on an unbounded domain D in R^d with Dirichlet boundary conditions (D may equal R^d in particular). Let u(x,E) be a solution of the Schrödin…
Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: some optimal results
Michael Christ, Alexander Kiselev
The absolutely continuous spectrum of one-dimensional Schrödinger operators is proved to be stable under perturbation by potentials satisfying mild decay conditions. In particular,…
Absolutely continuous spectrum of perturbed Stark operators
Alexander Kiselev
We prove new results on the stability of the absolutely continuous spectrum for perturbed Stark operators with decaying or satisfying certain smoothness assumption perturbation. We…
Preservation of the absolutely continuous spectrum of Schrödinger equation under perturbations by slowly decreasing potentials and a.e. convergence of integral operators
Alexander Kiselev
We prove new criteria of stability of the absolutely continuous spectrum of one-dimensional Schrödinger operators under slowly decaying perturbations. As applications, we show that…