Moment spaces of minimal dimension (Q1096827)

Let \(F_ n\) be the real linear space spanned by linearly independent real valued functions \(f_ i\), \(i=1,...,n\), defined on some set X. Denote by \(F_ n\cdot F_ n\) the real linear space spanned by the products \(f_ if_ j\), \(i,j=1,...,n\). The problem of characterizing the linear spaces \(F_ n\) which generate a space \(F_ n\cdot F_ n\) of minimal dimension 2n-1 is considered. The result of the author and \textit{E. Passow} [SIAM J. Math. Anal. 15, 166-169 (1984; Zbl 0533.41030)] is generalized.