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http://dx.doi.org/10.4134/JKMS.2005.42.4.723

THE QUARTIC MOMENT PROBLEM  

Li, Chun-Ji (Institute of System Science College of Sciences Northeastern University)
Lee, Sang-Hoon (Department of Mathematics University of Iowa)
Publication Information
Journal of the Korean Mathematical Society / v.42, no.4, 2005 , pp. 723-747 More about this Journal
Abstract
In this paper, we consider the quartic moment problem suggested by Curto-Fialkow[6]. Given complex numbers $\gamma{\equiv}{\gamma}^{(4)}\;:\;{\gamma00},\;{\gamma01},\;{\gamma10},\;{\gamma01},\;{\gamma11},\;{\gamma20},\;{\gamma03},\;{\gamma12},\;{\gamma21},\;{\gamma30},\;{\gamma04},\;{\gamma13},\;{\gamma22},\;{\gamma31},\;{\gamma40}$, with ${\gamma00},\;>0\;and\;{\gamma}_{ji}={\gamma}_{ij}$ we discuss the conditions for the existence of a positive Borel measure ${\mu}$, supported in the complex plane C such that ${\gamma}_{ij}=\int\;\={z}^i\;z^j\;d{\mu}(0{\leq}i+j{\leq}4)$. 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).
Keywords
the quartic moment problem; representing measure; flat extension;
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Times Cited By Web Of Science : 5  (Related Records In Web of Science)
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