相关论文: Ladder Operators for q-orthogonal Polynomials
We investigate the differential equation for the Jacobi-type polynomials which are orthogonal on the interval $[-1,1]$ with respect to the classical Jacobi measure and an additional point mass at one endpoint. This scale of higher-order…
The article presents a matrix differential operator and a pseudoinverse matrix differential operator for finding a particular solution to nonhomogeneous linear ordinary differential equations (ODE) with constant coefficients with special…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
We give a description of the field of rational natural differential invariants for a class of nonlinear differential operators of the third order on a two dimensional manifold and show their application to the equivalence problem of such…
We show some examples for uniformly monotone operators arising in weak formulation of nonlinear elliptic and parabolic problems. Besides the classical $p$-Laplacian some other less known examples are given which might be of interest because…
An effective method to obtain exact analytical solutions of equations describing the coherent dynamics of multilevel systems is presented. The method is based on the usage of orthogonal polynomials, integral transforms and their discrete…
Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well…
We derive explicit expressions for $q$-orthogonal polynomials arising in the enumeration of area-weighted Dyck paths with restricted height.
We review properties of q-orthogonal polynomials, related to their orthogonality, duality and connection with the theory of symmetric (self-adjoint) operators, represented by a Jacobi matrix. In particular, we show how one can naturally…
By solving an infinite nonlinear system of $q$-difference equations one constructs a chain of $q$-difference operators. The eigenproblems for the chain are solved and some applications, including the one related to $q$-Hahn orthogonal…
New nonlinear connection formulae of the q-orthogonal polynomials, such continuous q-Laguerre, continuous big q-Hermite, q-Meixner-Pollaczek and q-Gegenbauer polynomials, in terms of their respective classical analogues are obtained using a…
The one-dimensional Hubbard model is integrable in the sense that it has an infinite family of conserved currents. We explicitly construct a ladder operator which can be used to iteratively generate all of the conserved current operators.…
We compute arithmetic support of the formal deformations $D=P+tQ_1+t^2Q_2+...$ of the differential operator $P=(x\partial_x-r_1)...(x\partial_x-r_k)$, where $r_1,...,r_k\in\mathbb{Q}$ for sufficiently large primes $p$ in terms of the…
Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain…
In this paper, we introduce a notion of ladder representations for split odd special orthogonal groups and symplectic groups over a non-archimedean local field of characteristic zero. This is a natural class in the admissible dual which…
We discuss a fast approximate solution to the associated classical -- classical orthogonal polynomial connection problem. We first show that associated classical orthogonal polynomials are solutions to a fourth-order quadratic eigenvalue…
We construct a Heisenberg-like algebra for the one dimensional infinite square-well potential in quantum mechanics. The ladder operators are realized in terms of physical operators of the system as in the harmonic oscillator algebra. These…
We establish an analogue of the Bochner theorem for first order operators of Dunkl type, that is we classify all such operators having polynomial solutions. Under natural conditions it is seen that the only families of orthogonal…
We discuss initial value problems for time evolution equations in one dimensional space which are expressed by the lattice operators and propose some new equations to which complexity of solutions is of polynomial class. Novel type of…
Theory of differential operators on associative algebras is not extended to the non-associative ones in a straightforward way. We consider differential operators on Lie algebras. A key point is that multiplication in a Lie algebra is its…