Oleg Safronov

activity

20102024

collaborators

4 papers

math-ph2024

Monotonicity of the set of zeros of the Lyapunov exponent with respect to shift embeddings

Oleg Safronov

We consider the discrete Schrödinger operators with potentials whose values are read along the orbits of a shift of finite type. We study a certain subset of the collection of ener…

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.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.SP2010

Lower bounds on the eigenvalue sums of the Schrödinger operator and the spectral conservation law

Oleg Safronov

In the first part of the paper we consider the Schrödinger operator $- Δ - V (x), V > 0.$ We discuss the relation between the behavior of $V$ at the infinity and the properties of…