相关论文: A duality between Schroedinger operators on graphs…
The discrete spectrum of complex Jacobi matrices that are compact perturbations of the discrete laplacian is under consideration. The rate of stabilization for the the matrix entries which provides finiteness of the discrete spectrum and is…
We give an interpretation of the boson-fermion correspondence as a direct consequence of Jacobi-Trudi identity. This viewpoint enables us to construct from a generalized version of the Jacobi-Trudi identity the action of Clifford algebra on…
The Huttner$-$Barnett model is extended to a magnetodielectric medium by adding a new matter field to this model. The eigenoperators for the coupled system are calculated and electromagnetic field is written in terms of these operators. The…
We establish a strong-weak coupling duality between two types of free matrix models. In the large-N limit, the real-symmetric matrix model is dual to the quaternionic-real matrix model. Using the large-N conformal invariant collective field…
A general scheme for tridiagonalising differential, difference or q-difference operators using orthogonal polynomials is described. From the tridiagonal form the spectral decomposition can be described in terms of the orthogonality measure…
We propose a simple new combinatorial model to study spaces of acyclic Jacobi diagrams, in which they are identified with algebras of words modulo operations. This provides a starting point for a word-problem type combinatorial…
The boundedness of the Marcinkiewicz integrals associated with Schr\"{o}dinger operator from the localized Morrey-Campanato space to the localized Morrey-Campanato-BLO space is established. Similar results for the Marcinkiewicz integrals…
We give sufficient conditions for essential self-adjointness of magnetic Schr\"odinger operators on locally finite graphs. Two of the main theorems of the present paper generalize recent results of Torki-Hamza.
A class of state models, called Kronecker-Weierstrass models (or, simply, KW-models), is introduced, and the state representation problem for linear differential systems is studied in the context of these models. It is shown, in particular,…
We study $C_{0}$-operators relative to a multiply connected domain using a substitute of the characteristic function. This method allows us to prove certain relations between the Jordan model of an operator and that of its restriction to an…
We consider magnetic Schroedinger operators on quantum graphs with identical edges. The spectral problem for the quantum graph is reduced to the discrete magnetic Laplacian on the underlying combinatorial graph and a certain Hill operator.…
We consider two-sided Jacobi matrices whose coefficients are obtained by continuous sampling along the orbits of a homeomorphim of a compact metric space. Given an ergodic probability measure, we study the topological structure of the…
Is is shown in this paper that there is a connection between the Riemann zeta-function $\zf$ and the classical Jacobi's polynomials, i.e. the Legendre polynomials, Chebyshev polynomials of the first and the second kind,...
We recall criteria on the spectrum of Jacobi matrices such that the corresponding isospectral torus consists of periodic operators. Motivated by those known results for Jacobi matrices, we define a new class of operators called GMP…
Intertwining relations for $N$-particle Calogero-like models with internal degrees of freedom are investigated. Starting from the well known Dunkl-Polychronakos operators, we construct new kind of local (without exchange operation)…
We consider the dynamic problems for the discrete systems with discrete time associated with finite and semi-infinite Jacobi matrices. The result of the paper is a procedure of association of special Hilbert spaces of functions, namely de…
The paper is a continuation of the study started in \cite{Yorzh1}. Schrodinger operators on finite compact metric graphs are considered under the assumption that the matching conditions at the graph vertices are of $\delta$ type. Either an…
Based on \cite{DH94}, we introduce a bijective correspondence between first order differential calculi and the graph structure of the symmetric lattice that allows one to encode completely the interconnection structure of the graph in the…
We review some recent results and announce some new ones on the problem of the existence of ground states for the Nonlinear Schr\"odinger Equation on graphs endowed with vertices where the matching condition, instead of being free (or…
Schr\"odinger operators often display singularities at the origin, the Coulomb problem in atomic physics or the various matter coupling terms in the Friedmann-Robertson-Walker problem being prominent examples. For various applications it…