Spectral analysis and synthesis on multivariate polynomial hypergroups

Abstract

Let K be a countable set equipped with the discrete topology and let d be a positive integer. We consider a set (Q _x ) _x∈K of polynomials in d complex variables. If for any nonnegative integer n the symbol K _n denotes the set of all elements x in K for which the degree of Q_x is not greater than n, then we suppose that the polynomials Q_x with x in K_n form a basis for all polynomials of degree not greater than n.