ABSTRACT
This chapter contains three subsections. The first one summaries the theorems on orthogonal polynomials in several variables, the second one contains a characterization of centrally symmetric linear functionals, and the third one collects various lemmas. In contrast to the study of special systems, the chapter is concerned with the general theory; that is, properties shared by every system of orthogonal polynomials. The spectral theorem for a commuting family of self-adjoint operators has been used to study the integral representation of the linear functional in Favard’s theorem. A central symmetric L has a relatively simple structure which allows to get more information about the structure of orthogonal polynomials.
