The quartic moment problem
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Abstract
In this paper, we consider the quartic moment problem suggested byCurto-Fialkowcite{CuF4}. Given complex numbers gamma equivgamma ^{(4)}:gamma _{00},gamma _{01},gamma _{10}, gamma_{02},gamma _{11},gamma _{20},gamma _{03}, gamma_{12},gamma _{21},gamma _{30},gamma _{04},gamma _{13},gamma_{22},gamma _{31},gamma _{40}, with gamma _{00}>0 andgamma _{ji}=bar{gamma}_{ij}, we discuss the conditions forthe existence of a positive Borel measure mu , supportedin the complex plane mathbb{C} such that gamma _{ij}=int bar{z}%^{i}z^{j}dmu (0leq i+jleq 4). We obtain sufficientconditions for flat extension of the quartic moment matrix M(2).Moreover, we examine the existence of flat extensions for nonsingular positive quartic moment matrices $M(2).
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