Related papers: The direct spectral problem for indefinite canonic…
We study the non-selfadjoint Dirac system on a finite interval having non-integrable regular singularities in interior points with additional matching conditions at these points. Properties of spectral characteristics are established, and…
Dynamical canonical systems and their connections with the classical (spectral) canonical systems are considered. We construct B\"acklund-Darboux transformation and explicit solutions of the dynamical canonical systems. We study also those…
In the paper the conditions are obtained providing existence and uniqueness of the regular solution of the boundary problem for class of the second order homogeneous operator-differential equation with singular coefficients. High term of…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
We investigate the discrete spectrum of the Hamiltonian describing a quantum particle living in the two-dimensional straight strip. We impose the combined Dirichlet and Neumann boundary conditions on different parts of the boundary. Several…
Effective bounds for the finite number of surjective holomorphic maps between canonically polarized compact complex manifolds of any dimension with fixed domain are proven. Both the case of a fixed target and the case of varying targets are…
We study the Hamiltonian formulation for a parametrized scalar field in a regular bounded spatial region subject to Dirichlet, Neumann and Robin boundary conditions. We generalize the work carried out by a number of authors on parametrized…
We propose a formalism to study dynamical properties of a quantum many-body system in the thermodynamic limit by studying a finite system with infinite boundary conditions (IBC) where both finite size effects and boundary effects have been…
The path integral formulation of constrained systems leads to obtain the equations of motion as total differential equations in many variables. If these equations are integrable then one can constuct a valid and a canonical phase space…
An abstract linking result for Cerami sequences is proved without the Cerami condition. It is applied directly in order to prove the existence of critical points for a class of indefinite problems in infinite dimensional Hilbert Spaces. The…
We consider integrable models of the Haldane-Shastry type with open boundary conditions. We define monodromy matrices, obeying the reflection equation, which generate the symmetries of these models. Using a map to the Calogero-Sutherland…
We study a general discrete boundary value problem in Sobolev--Slobodetskii spaces in a plane quadrant and reduce it to a system of integral equations. We show a solvability of the system for a small size of discreteness starting from a…
We extend and improve the existing characterization of the dynamics of general quadratic real polynomial maps with coefficients that depend on a single parameter $\lambda$, and generalize this characterization to cubic real polynomial maps,…
This note is devoted to inverse spectral problems for canonical Hamiltonian systems on the half-line. An approach to inverse spectral problems based on the use of truncated Toeplitz operators has been especially effective in the case when…
The initial-boundary value problem for the two-dimensional regular four-velocity discrete Boltzmann system is analyzed in a rectangle. The existence and uniqueness of a classical global positive solution, bounded with its first partial…
It has been known that there exists a canonical system for every finite real reflection group. The first and the third authors obtained an explicit formula for a canonical system in the previous paper. In this article, we first define…
We study discrete fixed point sets of holomorphic self-maps of complex manifolds. The main attention is focused on the cardinality of this set and its configuration. As a consequence of one of our observations, a bounded domain in ${\Bbb…
A waveguide coincides with a three-dimensional domain G having finitely many cylindrical outlets to infinity; the boundary of G is smooth. In G, we consider the stationary Maxwell system with real spectral parameter k and identity matrices…
A Lagrangian system with singularities is considered. The configuration space is a non-compact manifold that depends on time. A set of periodic solutions has been found.
Canonical forms are central to the analytical understanding of tensor network states, underpinning key results such as the complete classification of one-dimensional symmetry-protected topological phases within the matrix product state…