Orthogonal polynomials associated with some modifications of a linear functional

Abstract

In this paper we study properties of a linear functional obtained by addition of the derivative of a Dirac mass to a regular linear functional. We give a necessary and sufficient condition for the regularity of the new functional. The coefficients of the second order recurrence relation, satisfied by the corresponding sequence of orthogonal polynomials, are given explicitly. In the semi-classical case, we classify the new linear functional in terms of the mass point. Finally, we apply the above results to Hermite polynomials.

Keywords:

• Linear functionals
• orthogonal polynomials
• distributions

AMS:

• 33A65