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....
Results and conjectures about order Lyness' difference equation in , with a particular study of the case .
Results on the deficiencies of some differential-difference polynomials of meromorphic functions
In this paper, we study the relation between the deficiencies concerning a meromorphic function f(z), its derivative f′(z) and differential-difference monomials f(z)mf(z+c)f′(z), f(z+c)nf′(z), f(z)mf(z+c). The main results of this paper are listed as follows: Let f(z) be a meromorphic function of finite order satisfying lim sup r→+∞ T(r, f) T(r, f ′ ) <+∞, and c be a non-zero complex constant, then δ(∞, f(z)m f(z+c)f′(z))≥δ(∞, f′) and δ(∞,f(z+c)nf′(z))≥ δ(∞, f′). We also investigate the value...
Resurgence relations for classes of differential and difference equations
Riccati matrix differential equation and the discrete order preserving property
In this paper we recall discrete order preserving property related to the discrete Riccati matrix equation. We present results obtained by applying this property to the solutions of the Riccati matrix differential equation.
Ruelle operator with nonexpansive IFS
The Ruelle operator and the associated Perron-Frobenius property have been extensively studied in dynamical systems. Recently the theory has been adapted to iterated function systems (IFS) , where the ’s are contractive self-maps on a compact subset and the ’s are positive Dini functions on X [FL]. In this paper we consider Ruelle operators defined by weakly contractive IFS and nonexpansive IFS. It is known that in such cases, positive bounded eigenfunctions may not exist in general. Our theorems...