Related papers: Discrete Dirac systems on the semiaxis: rational r…
We show that for general-type self-adjoint and skew-self-adjoint Dirac systems on the semi-axis Weyl functions are unique analytic extensions of the reflection coefficients. New results on the extension of the Weyl functions to the real…
New formulas on the inverse problem for the continuous skew-self-adjoint Dirac type system are obtained. For the discrete skew-self-adjoint Dirac type system the solution of a general type inverse spectral problem is also derived in terms…
We consider discrete Dirac systems as an alternative (to the famous Szeg\H{o} recurrencies and matrix orthogonal polynomials) approach to the study of the corresponding block Toeplitz matrices. We prove an analog of the Christoffel--Darboux…
Procedures to recover explicitly discrete and continuous skew-selfadjoint Dirac systems on semi-axis from rational Weyl matrix functions are considered. Their stability is shown. Some new facts on asymptotics of pseudo-exponential…
Discrete Dirac type self-adjoint system is equivalent to the block Szeg\"o recurrence. Representation of the fundamental solution is obtained, inverse problems on the interval and semi-axis are solved. A Borg-Marchenko type result is…
In this paper we study direct and inverse problems for discrete and continuous time skew-selfadjoint Dirac systems with rectangular (possibly non-square) pseudo-exponential potentials. For such a system the Weyl function is a strictly…
We consider discrete self-adjoint Dirac systems determined by the potentials (sequences) $\{C_k\}$ such that the matrices $C_k$ are positive definite and $j$-unitary, where $j$ is a diagonal $m\times m$ matrix and has $m_1$ entries $1$ and…
A non-classical Weyl theory is developed for skew-self-adjoint Dirac systems with rectangular matrix potentials. The notion of the Weyl function is introduced and direct and inverse problems are solved. A Borg-Marchenko type uniqueness…
Self-adjoint Dirac systems and subclasses of canonical systems, which generalize Dirac systems are studied. Explicit and global solutions of direct and inverse problems are obtained. A local Borg-Marchenko-type theorem, integral…
A transfer matrix function representation of the fundamental solution of the general-type discrete Dirac system, corresponding to rectangular Schur coefficients and Weyl functions, is obtained. Connections with Szeg\"o recurrence, Schur…
We establish simple connections between response functions of the dynamical Dirac systems and $A$-amplitudes and Weyl functions of the spectral Dirac systems. Using these connections we propose a new and rigorous procedure to recover a…
We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing and focusing nonlinear Schr\"odinger equation, of relevance…
We derive dispersion estimates for solutions of a one-dimensional discrete Dirac equations with a potential. In particular, we improve our previous result, weakening the conditions on the potential. To this end we also provide new results…
We present a method of constructing discrete integrable systems with crystallographic reflection group (Weyl) symmetries, thus clarifying the relationship between different discrete integrable systems in terms of their symmetry groups.…
A discrete analog of a skew selfadjoint canonical (Zakharov-Shabat or AKNS) system with a pseudo-exponential potential is introduced. For the corresponding Weyl function the direct and inverse problem are solved explicitly in terms of three…
In this paper, we find a polynomial-type Jost solution of a self-adjoint matrix-valued discrete Dirac system. Then we investigate analytical properties and asymptotic behavior of this Jost solution. Using the Weyl compact perturbation…
Weyl theory for Dirac systems with rectangular matrix potentials is non-classical. The corresponding Weyl functions are rectangular matrix functions. Furthermore, they are non-expansive in the upper semi-plane. Inverse problems are treated…
We characterize the set of rectangular Weyl matrix functions corresponding to Dirac systems with locally square-integrable potentials on a semi-axis and demonstrate a new way to recover the locally square-integrable potential from the Weyl…
A new class of representations of affine Weyl groups on rational functions are constructed, in order to formulate discrete dynamical systems associated with affine root systems. As an application, some examples of difference and…
We investigate the non-Fermi-liquid behaviors of the 2D and 3D Dirac/Weyl systems with low-order and higher order dispersion. The self-energy correction, symmetry, free energy, optical conductivity, density of states, and spectral function…