Best interpolation with polynomials lacking the linear term (Q1174314)

The following theorem is proved. For \(n\geq 2\) one considers the space of polynomials spanned by \(1,t^ 2,\ldots,t^{t+1}\). Optimal interpolation with this space on an interval \([a,b]\), with \(0<a<b\), and with nodes \(t_ 0,t_ 1,\ldots,t_ n\), satisfying the relations: \(a=t_ 0<t_ 1<\cdots<t_ n=b\), is characterized by the known equi-oscillation properties (Bernstein-Erdős conditions), and the nodes \(t_ 0,t_ 1,\ldots,t_ n\) are uniquely determined.