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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)
  • 발행 : 2005.07.01

초록

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).

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참고문헌

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피인용 문헌

  1. A Cyclic Subnormal Completion of Complex Data vol.54, pp.2, 2014, https://doi.org/10.5666/KMJ.2014.54.2.157
  2. Positivity of Riesz functionals and solutions of quadratic and quartic moment problems vol.258, pp.1, 2010, https://doi.org/10.1016/j.jfa.2009.09.015