THE FLAT EXTENSION OF NONSINGULAR EMBRY MOMENT MATRICES E(3)

摘要

Let gamma((n) ) {gamma(ij)} (0 <= i+j <= 2n, vertical bar i-j vertical bar <= n) be a sequence in the complex number set C and let E (n) be the Embry truncated moment matrices corresponding from gamma((n)). For an odd number n, it is known that gamma((n)) has a rank E(n)-atomic representing measure if and only if E(n) >= 0 and E(m) admits a flat extension E (n + 1). In this paper we suggest a related problem: if E(n) is positive and nonsingular, does E(n) have a flat extension E(n+1)? and give a negative answer in the case of E(3). And we obtain some necessary conditions for positive and nonsingular matrix E (3), and also its sufficient conditions.