Zobrazeno 1 - 10
of 42
pro vyhledávání: '"47E05, 34L40"'
Autor:
Lunyov, Anton A., Malamud, Mark M.
The paper is concerned with the completeness property of the system of root vectors of a boundary value problem for the following $2 \times 2$ Dirac type equation $$ L y = -i B^{-1} y' + Q(x) y = \lambda y , \quad y= {\rm col}(y_1, y_2), \quad x \in
Externí odkaz:
http://arxiv.org/abs/2312.15933
Autor:
Lunyov, Anton A., Malamud, Mark M.
The paper is concerned with the following $n\times n$ Dirac type equation$$Ly=-iB(x)^{-1}(y'+Q(x)y)=\lambda y, \quad B(x)=B(x)^*,\quad y={\rm col}(y_1,\ldots,y_n),\quad x\in[0,\ell],$$ on a finite interval $[0,\ell]$. Here $Q$ is a summable potential
Externí odkaz:
http://arxiv.org/abs/2112.07248
Autor:
Lunyov, Anton A., Malamud, Mark M.
The paper is concerned with the stability property under perturbation $Q\to\widetilde Q$ of different spectral characteristics of a BVP associated in $L^2([0,1];\Bbb C^2)$ with the following $2\times2$ Dirac type equation $$L_U(Q)y=-iB^{-1}y'+Q(x)y=\
Externí odkaz:
http://arxiv.org/abs/2012.11170
Autor:
Arslan, İlker
The one-dimensional Dirac operator with periodic potential $V=\begin{pmatrix} 0 & \mathcal{P}(x) \\ \mathcal{Q}(x) & 0 \end{pmatrix}$, where $\mathcal{P},\mathcal{Q}\in L^2([0,\pi])$ subject to periodic, antiperiodic or a general strictly regular bou
Externí odkaz:
http://arxiv.org/abs/1602.01290
Autor:
Lunyov, Anton A., Malamud, Mark M.
The paper is concerned with the Riesz basis property of a boundary value problem associated in $L^2[0,1] \otimes \mathbb{C}^2$ with the following $2 \times 2$ Dirac type equation $$ L y = -i B^{-1} y' + Q(x) y = \lambda y, \quad B = \begin{pmatrix} b
Externí odkaz:
http://arxiv.org/abs/1504.04954
Autor:
Mityagin, Boris
We consider the operator $ L = - (d/dx)^2 + x^2 y + w(x) y , y \in L^2(\mathbb{R}) $, where $ w(x) = s [ \delta(x - b) - \delta(x + b)], b \neq 0,$ real, $s \in \mathbb{C}$. This operator has a discrete spectrum: eventually the eigenvalues are simple
Externí odkaz:
http://arxiv.org/abs/1407.4153
Autor:
Djakov, Plamen, Mityagin, Boris
Consider the Hill operator $L(v) = - d^2/dx^2 + v(x) $ on $[0,\pi]$ with Dirichlet, periodic or antiperiodic boundary conditions; then for large enough $n$ close to $n^2 $ there are one Dirichlet eigenvalue $\mu_n$ and two periodic (if $n$ is even) o
Externí odkaz:
http://arxiv.org/abs/1403.2973
Autor:
Anahtarci, Berkay, Djakov, Plamen
The one-dimensional Dirac operator \begin{equation*} L = i \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \frac{d}{dx} +\begin{pmatrix} 0 & P(x) \\ Q(x) & 0 \end{pmatrix}, \quad P,Q \in L^2 ([0,\pi]), \end{equation*} considered on $[0,\pi]$ with perio
Externí odkaz:
http://arxiv.org/abs/1312.2219
Autor:
Djakov, Plamen, Mityagin, Boris
Let $L$ be the Hill operator or the one dimensional Dirac operator on the interval $[0,\pi].$ If $L$ is considered with Dirichlet, periodic or antiperiodic boundary conditions, then the corresponding spectra are discrete and for large enough $|n|$ cl
Externí odkaz:
http://arxiv.org/abs/1309.1751
Autor:
Djakov, Plamen, Mityagin, Boris
We consider the Hill operator $$ Ly = - y^{\prime \prime} + v(x)y, \quad 0 \leq x \leq \pi, $$ subject to periodic or antiperiodic boundary conditions ($bc$) with potentials of the form $$ v(x) = a e^{-2irx} + b e^{2isx}, \quad a, b \neq 0, r,s \in \
Externí odkaz:
http://arxiv.org/abs/1210.3907