THE QUARTIC MOMENT PROBLEM

Title & Authors
THE QUARTIC MOMENT PROBLEM
Li, Chun-Ji; Lee, Sang-Hoon;

Abstract
In this paper, we consider the quartic moment problem suggested by Curto-Fialkow[6]. Given complex numbers $\small{\gamma{\equiv}{\gamma}^{(4)}\;:\;{\gamma00},\;{\gamma01},\;{\gamma10},\;{\gamma01},\;{\gamma11},\;{\gamma20},\;{\gamma03},\;{\gamma12},\;{\gamma21},\;{\gamma30},\;{\gamma04},\;{\gamma13},\;{\gamma22},\;{\gamma31},\;{\gamma40}}$, with ${\gamma00},\;>0\;and\;{\gamma}_{ji}={\gamma}_{ij}$ we discuss the conditions for the existence of a positive Borel measure $\small{{\mu}}$, supported in the complex plane C such that $\small{{\gamma}_{ij}=\int\;\={z}^i\;z^j\;d{\mu}(0{\leq}i+j{\leq}4)}$. We obtain sufficient conditions 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).ᬊ꼀Ѐ〷〻ഀ䝥湥牡氠睯牫猀
Keywords
the quartic moment problem;representing measure;flat extension;
Language
English
Cited by
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