arXiv subjects

S. A. Stepin

Publications and source records attributed to S. A. Stepin.

4 recordsLinked to original sources

arXiv2017

Complete wave operators in non-selfadjoint Kato model of smooth perturbation theory

Subject of the paper deals with the perturbation theory of linear operators acting in Hilbert space. For a certain class of perturbations the question is considered about existence of transformation operators implementing linear similarity of perturbed and unperturbed operators. In this context some results of complex analysis prove to be useful as well as the relationship with the theory of operator semi-groups.

math.FA↗

arXiv2014

Complex potentials: bound states, quantum dynamics and wave operators

Schrödinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated. Wave operators are constructed and a criterion is established for the similarity of perturbed and free propagators.

math.SP↗

arXiv2013

An upper bound for the number of eigenvalues of non-selfadjoint Schrödinger operator

Estimates for the total multiplicity of eigenvalues for Schrödinger operator are established in the case of compactly supported or exponentially decreasing complex-valued potential.

math.SP↗

arXiv2013

Scattering and bound states for nonselfadjoint Schrödinger operator

Spectral components of one-dimensional Schrödinger operator with complex potential are investigated. An effective upper bound for the total number of eigenvalues and spectral singularities is established. For dissipative Schrödinger operator sufficient condition is found which guarantees the absence of singular component in the continuous spectrum and spectral decomposition is exposed.

math.CA↗