Abstract. Properties of reproducing kernel function, Bessel's inequality, Parseval's identity in terms of an orthogonal basis of the space of all polynomials in $d$, where $d\in N\setminus\{1\} $, variables are studied.

AMS Subject Classification (1991): 42C05, 33C50

Keyword(s): multivariate orthogonal polynomials

Received February 26, 1998 and in revised form September 21, 1998. (Registered under 2679/2009.)