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

摘要

Let γ (n) ≡ {γ ij }(0 ≤ i+j ≤ 2n, |i?j| ≤ n) be a sequence in the complex number set C and let E (n) be the Embry truncated moment matrices corresponding from γ (n) . For an odd number n, it is known that γ (n) has a rank E (n)-atomic representing measure if and only if E(n) ≥ 0 and E(n) 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.