14 citations · 59 across the 12 of their papers we have counts for
14 papers
Semigroup properties of Schrödinger operators with complex singular potentials
Vladimir Mikhailets, Volodymyr Molyboga
In the complex Hilbert space on the half-line , we investigate non-symmetric Schrödinger operators \[ Su = -u'' + qu, \qquad u(0) =…
Uniqueness problem for accretive Schrödinger operators with complex singular coefficients
Vladimir Mikhailets, Volodymyr Molyboga
This paper studies the uniqueness problem for the one-dimensional Schrödinger operator associated with the formal differential expression \begin{equation*} l[u] =-u''+qu + i[(ru)'+…
Povzner-Wienholtz-type theorems for Sturm-Liouville operators with singular coefficients
Andrii Goriunov, Vladimir Mikhailets, Volodymyr Molyboga
We introduce and investigate symmetric operators associated in the complex Hilbert space with a formal differential expression \[l[u] :=-(pu')'+qu + i((ru)'…
Schrödinger operators with measure-valued potentials: semiboundedness and spectrum
Vladimir Mikhailets, Volodymyr Molyboga
We study the 1-D Schrödinger operators in Hilbert space with real-valued Radon measure , as potentials. New sufficie…
Spectral gaps of the Hill--Schrödinger operators with distributional potentials
Vladimir Mikhailets, Volodymyr Molyboga
The paper studies the Hill--Schrödinger operators with potentials in the space . The main results completely describe the sequ…
Uniform estimates for the semi-periodic eigenvalues of the singular differential operators
Vladimir Mikhailets, Volodymyr Molyboga
Let , , and be a 1-periodic complex-valued distribution in the negative Sobolev space . The singular non-self-adjoint eigenvalue probl…
Singular eigenvalue problems on the circle
Vladimir Mikhailets, Volodymyr Molyboga
The eigenvalue problem on the circle for the non-self-adjoint operators , with singular complex-valued 2-periodic distr…
Estimates for Periodic Eigenvalues of the Differential Operator with V -- Distribution
Volodymyr Molyboga
The periodic eigenvalue problem for the differential operator is studied for complex-valued distribution V in the Sobolev space $H^{-mα}_{per}[-1,1]\;(m\…
Remarks on Schrödinger operators with singular matrix potentials
Vladimir Mikhailets, Volodymyr Molyboga
In this paper the asymmetric generalization of the Glazman-Povzner-Wienholtz theorem is proved for one-dimensional Schrödinger operators with strongly singular matrix potentials fr…
Schrödinger operators with complex singular potentials
Vladimir Mikhailets, Volodymyr Molyboga
We study one-dimensional Schrödinger operators on the space with potentials being complex-valued generalized functions from the negative spa…
Smoothness of Hill's potential and lengths of spectral gaps
Vladimir Mikhailets, Volodymyr Molyboga
Let be the lengths of spectral gaps in a continuous spectrum of the Hill-Schrödinger operators S(q)u=-u''+q(x)u,\quad x\in \mathbb{R}, with 1-periodic…
Hill's potentials in Hörmander spaces and their spectral gaps
Vladimir Mikhailets, Volodymyr Molyboga
In the paper we study the behaviour of the lengths of spectral gaps in a continuous spectrum of the Hill-Schrödinger operators $$S(q)u=-u"+q(x)u,\q…
One-dimensional Schrödinger operators with singular periodic potentials
V. Mikhailets, V. Molyboga
We study the one-dimensional Schrödinger operators with -periodic real-valued singular potentials $q(x)\in H_{\o…
Singularly perturbed periodic and semiperiodic differential operators
V. A. Mikhailets, V. M. Molyboga
Qualitative and spectral properties of the form-sums S_{\pm}(V):=D_{\pm}^{2m}\dotplus V(x),\quad m\in \mathbb{N}, in the Hilbert space are studied. Here the periodic $…