Zobrazeno 1 - 10
of 30
pro vyhledávání: '"Molyboga, Volodymyr"'
We introduce and investigate symmetric operators $L_0$ associated in the complex Hilbert space $L^2(\mathbb{R})$ with a formal differential expression \[l[u] :=-(pu')'+qu + i((ru)'+ru') \] under minimal conditions on the regularity of the coefficient
Externí odkaz:
http://arxiv.org/abs/2110.11750
Publikováno v:
Methods Funct. Anal. Topology 24 (2018), no. 3, 240-254
We study the 1-D Schr\"odinger operators in Hilbert space $L^{2}(\mathbb{R})$ with real-valued Radon measure $q'(x)$, $q\in \mathrm{BV}_{loc}(\mathbb{R})$ as potentials. New sufficient conditions for minimal operators to be bounded below and selfadjo
Externí odkaz:
http://arxiv.org/abs/1810.06363
Publikováno v:
Methods Funct. Anal. Topology 20 (2014), no. 4, 321-327
The paper studies the Hill--Schr\"odinger operators with potentials in the space $H^\omega \subset H^{-1}\left(\mathbb{T}, \mathbb{R}\right)$. The main results completely describe the sequences arising as the lengths of spectral gaps of these operato
Externí odkaz:
http://arxiv.org/abs/1501.00712
Publikováno v:
Methods Funct. Anal. Topology 10 (2004), no. 3, 44-53
The eigenvalue problem on the circle for the non-self-adjoint operators $L_{m}(V)=(-1)^{m}\frac{d^{2m}}{dx^{2m}}+V$, $m\in \mathbb{N}$ with singular complex-valued 2-periodic distributions $V\in H_{per}^{-m}[-1,1]$ is studied. Asymptotic formulae for
Externí odkaz:
http://arxiv.org/abs/1403.2643
Publikováno v:
Methods Funct. Anal. Topology 10 (2004), no. 4, 30-57
Let $m\in \mathbb{N}$, $\alpha\in[0,1]$, and $V$ be a 1-periodic complex-valued distribution in the negative Sobolev space $H^{-m\alpha}[0,1]$. The singular non-self-adjoint eigenvalue problem $D^{2m}u+V u=\lambda u$, $D=-i d/dx$, with semi-periodic
Externí odkaz:
http://arxiv.org/abs/1403.2655
Autor:
Molyboga, Volodymyr
Publikováno v:
Methods Funct. Anal. Topology 9 (2003), no. 2, 163-178
The periodic eigenvalue problem for the differential operator $(-1)^{m}d^{2m}/dx^{2m}+V$ is studied for complex-valued distribution V in the Sobolev space $H^{-m\alpha}_{per}[-1,1]\;(m\in\mathbb{N},\; 0\leq\alpha<1)$. The following result is shown: T
Externí odkaz:
http://arxiv.org/abs/1403.2627
Publikováno v:
Methods Funct. Anal. Topology, vol. 19 (2013), no. 2, 161-167
In this paper the asymmetric generalization of the Glazman-Povzner-Wienholtz theorem is proved for one-dimensional Schr\"{o}dinger operators with strongly singular matrix potentials from the space $H_{loc}^{-1}(\mathbb{R}, \mathbb{C}^{m\times m})$. T
Externí odkaz:
http://arxiv.org/abs/1306.0439
Publikováno v:
Methods Funct. Anal. Topology, vol. 19 (2013), no. 1, 16-28
We study one-dimensional Schr\"{o}dinger operators $\mathrm{S}(q)$ on the space $L^{2}(\mathbb{R})$ with potentials $q$ being complex-valued generalized functions from the negative space $H_{unif}^{-1}(\mathbb{R})$. Particularly the class $H_{unif}^{
Externí odkaz:
http://arxiv.org/abs/1306.0435
Publikováno v:
Oper. Theory Adv. Appl. 221 (2012), 469-479
Let ${\gamma_q(n)}_{n \in \mathbb{N}}$ be the lengths of spectral gaps in a continuous spectrum of the Hill-Schr\"odinger operators S(q)u=-u''+q(x)u,\quad x\in \mathbb{R}, with 1-periodic real-valued potentials $q \in L^{2}(\mathbb{T})$. Let weight f
Externí odkaz:
http://arxiv.org/abs/1003.5000
Publikováno v:
Methods Funct. Anal. Topology 17 (2011), no. 3, 235-243
In the paper we study the behaviour of the lengths of spectral gaps $\{\gamma_{q}(n)\}_{n\in \mathbb{N}}$ in a continuous spectrum of the Hill-Schr\"{o}dinger operators $$S(q)u=-u"+q(x)u,\quad x\in\mathbb{R},$$ with 1-periodic real-valued distributio
Externí odkaz:
http://arxiv.org/abs/0905.4655