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. To cite this article: B.G. Giraud et al., C. R. Physique 5 (2004).