Local representation of functions of D variables by means of discrete orthogonal polynomials

Discrete normalized orthogonal polynomials of D variables are defined by means of the orthogonal polynomials of a discrete variable introduced by Tchebychef. If a function of D variables is given by its values on a mesh, it may easily be expanded into a series of these polynomials of D variables. A truncation of this expansion is optimal in the sense of the method of least squares. The expansion may be used to study properties of the original function such a local extrema.