23 citations · 61 across the 21 of their papers we have counts for
21 papers
Riesz basis property of Hill operators with potentials in weighted spaces
Plamen Djakov, Boris Mityagin
Consider the Hill operator on with Dirichlet, periodic or antiperiodic boundary conditions; then for large enough close to there are…
Asymptotics of spectral gaps of 1D Dirac operator with two exponential terms potential
Berkay Anahtarci, Plamen Djakov
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…
Asymptotic formulas for spectral gaps and deviations of Hill and 1D Dirac operators
Plamen Djakov, Boris Mityagin
Let be the Hill operator or the one dimensional Dirac operator on the interval If is considered with Dirichlet, periodic or antiperiodic boundary conditions, then…
Divergence of spectral decompositions of Hill operators with two exponential term potentials
Plamen Djakov, Boris Mityagin
We consider the Hill operator subject to periodic or antiperiodic boundary conditions () with potentials of the f…
Combinatorial identities related to eigenfunction decompositions of Hill operators: Open Questions
Plamen Djakov, Boris Mityagin
We formulate several open questions related to enumerative combinatorics, which arise in the spectral analysis of Hill operators with trigonometric polynomial potentials.
Improved asymptotics of the spectral gap for the Mathieu operator
Berkay Anahtarci, Plamen Djakov
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 $…