15 citations · 17 across the 4 of their papers we have counts for
5 papers
Duality of q-polynomials, orthogonal on countable sets of points
N. M. Atakishiyev, A. U. Klimyk
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 Jac…
A set of orthogonal polynomials, dual to alternative q-Charlier polynomials
N. M. Atakishiyev, A. U. Klimyk
The aim of this paper is to derive (by using two operators, representable by a Jacobi matrix) a family of q-orthogonal polynomials, which turn to be dual to alternative q-Charlier…
On q-orthogonal polynomials, dual to little and big q-Jacobi polynomials
N. M. Atakishiyev, A. U. Klimyk
This paper studies properties of q-Jacobi polynomials and their duals by means of operators of the discrete series representations for the quantum algebra U_q(su_{1,1}). Spectrum a…
Hamiltonian Type Operators in Representations of the Quantum Algebra U_q(su_{1,1})
N. M. Atakishiyev, A. U. Klimyk
We study some classes of symmetric operators for the discrete series representations of the quantum algebra U_q(su_{1,1}), which may serve as Hamiltonians of various physical syste…
Meixner Oscillators
Natig M. Atakishiyev, Elchin I. Jafarov, Shakir M. Nagiev +1
Meixner oscillators have a ground state and an `energy' spectrum that is equally spaced; they are a two-parameter family of models that satisfy a Hamiltonian equation with a {\it d…