O. Safronov

activity

20162022

collaborators

4 papers

math-ph2022

The rate of accumulation of negative eigenvalues to zero and the absolutely continuous spectrum

Oleg Safronov

For a bounded real-valued function $V$ on $R^{d}$ , we consider two Schrödinger operators $H_{+} = - Δ + V$ and $H_{-} = - Δ - V$ . We prove that if the negative spectra $H_{+}$ and $H_{-}$ are d…

math-ph2021

Absolutely continuous and pure point spectra of discrete operators with sparse potentials

S. Molchanov, O. Safronov, B. Vainberg

We consider the discrete Schrödinger operator $H = - Δ + V$ with a sparse potential $V$ and find conditions guaranteeing either existence of wave operators for the pair $H$ and $H_{0} = - Δ$ …

math.SP2018

Eigenvalue bounds for Stark operators with complex potentials

Evgeny Korotyaev, Oleg Safronov

We consider the 3-dimensional Stark operator perturbed by a complex-valued potential. We obtain an estimate for the number of eigenvalues of this operator as well as for the sum of…

math.SP2016

Eigenvalues of the bilayer graphene operator with a complex valued potential

Francesco Ferrulli, Ari Laptev, Oleg Safronov

We study the spectrum of a system of second order differential operator perturbed by a non-selfadjoint matrix valued potential. We prove that eigenvalues of the perturbed operator…