The factorization method for the Askey-Wilson polynomials.

A special Infeld-Hall factorization is given for the Askey-Wilson second order q-difference operator. It is then shown how to deducd a generalization of the corresponding Askey-Wilson polynomials

Discrete Darboux transformation for discrete polynomials of hypergeometric type

Darboux Transformation, well known in second order differential operator theory, is applied here to the difference equation satisfied by the discrete hypergeometric polynomials(Charlier, Meixner-Krawchuk, Hahn)

The set of Grigorian generalizing meromorphic functions extends the set of Bohr almost periodic meromorphic functions from a metric space onto a field

Thèse de doctorat annexe - UCL, 199

Variational q-calculus

AbstractWe propose q-versions of some basic concepts of continuous variational calculus such as the Euler–Lagrange equation and its applications to the isoperimetric, Lagrange and optimal control problems (“the maximum principle”), and also to the Hamilton systems and commutation equations

Discrete factorization techniques for orthogonal polynomials on lattices

Doctorat en sciences - UCL, 199

q-Non uniform difference calculus and classical integral inequalities

Abstract We first establish q-non uniform difference versions of the integral inequalities of Hölder, Cauchy–Schwarz, and Minkowski of classical mathematical analysis and then integral inequalities of Grönwall and Bernoulli based on the Lagrange method of linear q-non uniform difference equations of first order. Finally, we prove the Lyapunov inequality for the solutions of the q-non uniform Sturm–Liouville equation

Variational calculus on q-nonuniform lattices

Consiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7 , Rome / CNR - Consiglio Nazionale delle RichercheSIGLEITItal