L. Zelenko

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20152019

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math.SP2020

Criterion of holomorphy with respect to a coupling constant of continuous functions of a perturbed self-adjoint operator

Leonid Zelenko

Sufficient and necessary conditions on the spectral measure of a self-adjoint operator $A$ , acting in a Hilbert space, are obtained, under which for any continuous scalar function…

math.SP2020

Conditions for discreteness of the spectrum to Schrödinger operator via non-increasing rearrangement, Lagrangian relaxation and perturbations

Leonid Zelenko

This work is a continuation of our previos paper, where for the Schrödinger operator $H=-Δ+ V(\e)\cdot$ $(V(\e)\ge 0)$, acting in the space $L_{2} (R^{d}) (d \geq 3)$ , some sufficient c…

math.SP2019

Conditions for discreteness of the spectrum to multi-dimensional Schrödinger operator

Leonid Zelenko

This work is a continuation of our previos paper \cite{Zel1}, where for the the Schrödinger operator $H=-Δ+ V(\e)\cdot$ $(V(\e)\ge 0)$, acting in the space $L_{2} (R^{d}) (d \geq 3)$ , s…

math.SP2018

Conditions of discreteness of the spectrum for Schrödinger operator and some optimization problems for capacity and measures

Leonid Zelenko

For the the Schrödinger operator $H = - Δ + V (x) \cdot$ , acting in the space L_2(\R^d)\,(d\ge 3), with V(x)\ge 0 and V(\cdot)\in L_{1,loc}(\R^d), we obtain some constructive conditions…

math.SP2015

Virtual bound levels in a gap of the essential spectrum of the Schroedinger operator with a weakly perturbed periodic potential

Leonid Zelenko

In the space $L_{2} (R^{d})$ we consider the Schrödinger operator $H_{γ} = - Δ + V (x) \cdot + γ W (x) \cdot$ , where $V (x) = V (x_{1}, x_{2}, \dots, x_{d})$ is a periodic function with respect to all the variab…