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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 $$ v(x) = a e^{-2irx} + b e^{2isx}, \quad a, b \neq 0, r,s \in \
Externí odkaz:
http://arxiv.org/abs/1210.3907
Autor:
Djakov, Plamen, Mityagin, Boris
We formulate several open questions related to enumerative combinatorics, which arise in the spectral analysis of Hill operators with trigonometric polynomial potentials.
Externí odkaz:
http://arxiv.org/abs/1210.0835
Autor:
Anahtarci, Berkay, Djakov, Plamen
The Mathieu operator {equation*} L(y)=-y"+2a \cos{(2x)}y, \quad a\in \mathbb{C},\;a\neq 0, {equation*} considered with periodic or anti-periodic boundary conditions has, close to $n^2$ for large enough $n$, two periodic (if $n$ is even) or anti-perio
Externí odkaz:
http://arxiv.org/abs/1202.4623
Autor:
Aytuna, Aydin, Djakov, Plamen
We prove that if $(\varphi_n)_{n=0}^\infty, \; \varphi_0 \equiv 1, $ is a basis in the space of entire functions of $d$ complex variables, $d\geq 1,$ then for every compact $K\subset \mathbb{C}^d$ there is a compact $K_1 \supset K$ such that for ever
Externí odkaz:
http://arxiv.org/abs/1201.5607
Autor:
Djakov, Plamen, Mityagin, Boris
We study in various functional spaces the equiconvergence of spectral decompositions of the Hill operator $L= -d^2/dx^2 + v(x), $ $x \in [0,\pi], $ with $H_{per}^{-1} $-potential and the free operator $L^0=-d^2/dx^2, $ subject to periodic, antiperiod
Externí odkaz:
http://arxiv.org/abs/1110.6696
Autor:
Djakov, Plamen, Mityagin, Boris
For one-dimensional Dirac operators $$ Ly= i \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \frac{dy}{dx} + v y, \quad v= \begin{pmatrix} 0 & P \\ Q & 0 \end{pmatrix}, \;\; y=\begin{pmatrix} y_1 \\ y_2 \end{pmatrix}, $$ subject to periodic or antiperi
Externí odkaz:
http://arxiv.org/abs/1108.4225