Polynomial hypergroups in several variables (Q1203521)

The author introduces and studies hypergroups related to orthogonal polynomials in several variables. First, the notion of polynomial hypergroup in \(d\) variables is introduced and their dual space is determined and analyzed. Then, a list of very interesting examples is given: It contains the product of polynomial hypergroups in one variable, the disk polynomials, the Chebyshev polynomials in \(d\) variables. Finally, four examples are investigated (studied earlier by \textit{T. Koornwinder} [Theory Appl. Spec. Funct. 1975, 435-495 (1975; Zbl 0326.33002)]). For all these examples the dual space is determined explicitly.