Properties of solutions to nonlinear dynamic integral equations on time scales.
-dominant and -recessive matrix solutions for linear quantum systems.
q-Heat Operator and q-Poisson’s Operator
2000 Mathematics Subject Classification: 33D15, 33D90, 39A13In this paper we study the q-heat and q-Poisson’s operators associated with the q-operator ∆q (see[5]). We begin by summarizing some statements concerning the q-even translation operator Tx,q, defined by Fitouhi and Bouzeffour in [5]. Then, we establish some basic properties of the q-heat semi-group such as boundedness and positivity. In the second part, we introduce the q-Poisson operator P^t, and address its main properties. We show...
Quadratic forms as Lyapunov functions in the study of stability of solutions to difference equations.
Quantitative bounds for positive solutions of a Stević difference equation.
Quantum Painlevé equations: from continuous to discrete.
Quasi-adjoint third order difference equations: Oscillatory and asymptotic behavior.
Quasi-Fibonacci numbers of order 11.
Rate of convergence of solutions of rational difference equation of second order.
Recent results concerning dynamic equations on time scales.
Recurrence relations for the coefficients of expansions in classical orthogonal polynomials of a discrete variable
A method is given to find a recurrence relation for the coefficients of the series expansion of a function f with respect to classical orthogonal polynomials of a discrete variable, which follows from a linear difference equation satisfied by f.
Reducibility and stability results for linear system of difference equations.
Reducible Linear Difference Operators
Reduction of the modified Poincaré differential equation to Birkhoff matrix form.
Regularization of one class of difference equations.
Regularly varying solutions of second-order difference equations with arbitrary sign coefficient.
Relations between limit-point and Dirichlet properties of second-order difference operators.
Relative Differenzeneigenschaft
Representation of solutions of linear discrete systems with constant coefficients and pure delay.
Representations of quantum groups and (conditionally) invariant q-difference equations
We give a systematic discussion of the relation between q-difference equations which are conditionally -invariant and subsingular vectors of Verma modules over (the Drinfeld-Jimbo q-deformation of a semisimple Lie algebra over ℂg or ℝ). We treat in detail the cases of the conformal algebra, = su(2,2), and its complexification, = sl(4). The conditionally invariant equations are the q-deformed d’Alembert equation and a new equation arising from a subsingular vector proposed by Bernstein-Gel’fand-Gel’fand....