POSITIVE LAGRANGE POLYNOMIALS

In this paper we demonstrate the existence of a set of polynomials Pi , 1? i ? n , which are positive semi-definite on an interval [a , b] and satisfy, partially, the conditions of polynomials found in the Lagrange interpolation process. In other words, if a ? a1 ??? an ? b is a given finite sequence of real numbers, then Pi (a j ) ? ?ij (?ij is the Kronecker delta symbol ) ; moreover, the sum of Pi ʹs is identically 1.