Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A NOTE ON SINGULAR QUARTIC MOMENT PROBLEM

  • Li, Chun-Ji (Department of Mathematics, Yanbian University)
  • Published : 2000.02.01
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Abstract

Let ${\gamma}{\equiv}{\gamma}^{(2n)}$ denote a sequence of complex numbers ${\gamma}{00},{\gamma}{01},\cdots,{\gamma}0, 2n,...,{\gamma}{2n},0\;with\; {\gamma}{00}\;>\;0,{\gamma}{ji}={{\overline}{\gamma_{ij}}}$,and let K denote a closed subset of the complex plane C. The truncated K complex moment problem entails finding a positive Borel measure $\mu$ such that ${\gamma}{ij}={\int}{{\overline}{z}}^{i}z^{j}d{\mu}\;(0{\leq}\;i+j\;{\leq}\;2n)$ and supp ${\mu}{\subseteq}\;K$. If n=2, then is called the quartic moment problem. In this paper, we give partial solutions for the singular quartic moment problem with rank M(2)=5 and ${{\overline}{Z}}Z{\in}\;<1,Z,{{\overline}{Z}},Z^{2},{{\overline}{Z}}^2>$.

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References

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