V. Molyboga

activity

20072026

most citedSingular eigenvalue problems on the circle

14 citations · 59 across the 12 of their papers we have counts for

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10 papers · 1 filter

math.SP2026

Semigroup properties of Schrödinger operators with complex singular potentials

Vladimir Mikhailets, Volodymyr Molyboga

In the complex Hilbert space $L_{2} (R_{+})$ on the half-line $R_{+} = [0, \infty)$ , we investigate non-symmetric Schrödinger operators \[ Su = -u'' + qu, \qquad u(0) =…

math.SP2025

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)'+…

math.SP2021

Povzner-Wienholtz-type theorems for Sturm-Liouville operators with singular coefficients

Andrii Goriunov, Vladimir Mikhailets, Volodymyr Molyboga

We introduce and investigate symmetric operators $L_{0}$ associated in the complex Hilbert space $L^{2} (R)$ with a formal differential expression \[l[u] :=-(pu')'+qu + i((ru)'…

math.SP2018★ 2 cited

Schrödinger operators with measure-valued potentials: semiboundedness and spectrum

Vladimir Mikhailets, Volodymyr Molyboga

We study the 1-D Schrödinger operators in Hilbert space $L^{2} (R)$ with real-valued Radon measure $q^{'} (x)$ , $q \in BV_{l oc} (R)$ as potentials. New sufficie…

math.SP2015★ 1 cited

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 $H^{ω} \subset H^{- 1} (T, R)$ . The main results completely describe the sequ…

math.SP2013★ 6 cited

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…

math.SP2013★ 3 cited

Schrödinger operators with complex singular potentials

Vladimir Mikhailets, Volodymyr Molyboga

We study one-dimensional Schrödinger operators $S (q)$ on the space $L^{2} (R)$ with potentials $q$ being complex-valued generalized functions from the negative spa…

math.SP2010

Smoothness of Hill's potential and lengths of spectral gaps

Vladimir Mikhailets, Volodymyr Molyboga

Let $γ_{q} (n)_{n \in N}$ 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…

math.SP2009★ 3 cited

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 ${γ_{q} (n)}_{n \in N}$ in a continuous spectrum of the Hill-Schrödinger operators $$S(q)u=-u"+q(x)u,\q…

math.SP2008★ 7 cited

One-dimensional Schrödinger operators with singular periodic potentials

V. Mikhailets, V. Molyboga

We study the one-dimensional Schrödinger operators $S (q) u := - u " + q (x) u, u \in Dom (S (q)),$ with $1$ -periodic real-valued singular potentials $q(x)\in H_{\o…