Perturbations of discrete semiclassical functionals by dirac masses

Abstract

The effect of modifying linear functionals acting on the linear space of polynomials with complex coefficients by means of Dirac deltas has been extensively studied. In this paper we present some results concerning modifications of semi-classical functionals with respect to the generalized difference operator by means of Dirac deltas. Applications of these techniques to discrete orthogonal polynomials (e.g. Charlier, discrete Laguerre discrete Chebychev polynomials) in order to obtain similar properties to the continuous case are given.