Orthogonal polynomial sets with finite codimensions

We define sets of orthogonal polynomials which lack one or several degrees, because of a finite number of constraints. In particular, we are interested in a generalization of Hermite polynomials, governed by a constraint of zero average. These are of interest, for example, for the study of the Hohenberg-Kohn functional. In particular, they allow the calculation of potential perturbations which generate strictly proportional density perturbations. (C) 2004 Academie des sciences. Published by Elsevier SAS. All rights reserved.