Abstract
We give some characterization theorems for the D w -Laguerre-Hahn linear functionals and we extend the concept of the class of the usual Laguerre-Hahn functionals to the D w -Laguerre-Hahn functionals, recovering the classic results when w tends to zero. Moreover, we show that some transformations carried out on the D w -Laguerre-Hahn linear functionals lead to new D w -Laguerre-Hahn linear functionals. Finally, we analyze the class of the resulting functionals and we give some applications relative to the first associated Charlier, Meixner, Krawtchouk and Hahn orthogonal polynomials.