The Nonsingular Quartic Moment Problem

Moment problem is a classical problem which has been studied since the 19^th century ,with the importance of basic research,more and more attention has been paid to moment problem, in this paper, we consider the quartic moment problem suggested by Curto and Fialkow[17].Given complex numbersγ≡γ⁽⁴⁾:γ₀₀,γ₀₁,γ₁₀,γ₀₂,γ₁₁,γ₂₀,γ₀₃,γ₁₂,γ₂₁,γ₃₀,γ₀₄,γ₁₃,γ₂₂,γ₃₁,γ₄₀with γ₀₀>0, γ_ji=(γ_ji)|-, find a positive Borel measure μ such thatwe examine the existence of flat extensions for nonsingular positive quartic moment matrices M(2),give partil solutions for the nonsingular quatic moment problem with rank M(2) = 6 and examples are provided .