O. Safronov

activity

20092022

most citedEstimates for eigenvalues of the Schrödinger operator with a complex potential

56 citations · 65 across the 6 of their papers we have counts for

collaborators

9 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…

math.SP2016

On the number of eigenvalues of Schrödinger operators with complex potentials

Rupert L. Frank, Ari Laptev, Oleg Safronov

We study the eigenvalues of Schrödinger operators with complex potentials in odd space dimensions. We obtain bounds on the total number of eigenvalues in the case where $V$ decays…

math-ph2011★ 2 cited

Absolutely continuous spectrum of a typical Schrödinger operator with a slowly decaying potential

Oleg Safronov

We consider a family of multi-dimensional Schrödinger operators $- Δ + t V$ with a real $t$ . The potential $V$ in our model decays at infinity in a special way, so that it satisfies a…

math.SP2011★ 7 cited

Absolutely continuous spectrum of a one-paramentric family of Schrödinger operators

Oleg Safronov

We consider a family of operators $- Δ + t V$ with a slowly decaying and oscillating potential $V$ . We prove that the absolutely continuous spectrum of this operator is essentially s…

math-ph2009

On a sum rule for Schrödinger operators with complex potentials

Oleg Safronov

We study the distribution of eigenvalues of the one-dimensional Schrödinger operator with a complex valued potential $V$ . We prove that if $∣ V ∣$ decays faster than the Coulomb pote…

math-ph2009★ 56 cited

Estimates for eigenvalues of the Schrödinger operator with a complex potential

Oleg Safronov

We study the distribution of eigenvalues of the Schrödinger operator with a complex valued potential $V$ . We prove that if $∣ V ∣$ decays faster than the Coulomb potential, then all…