Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The quintic complex moment problem   Let $\gamma^{(m)} \equiv \{ \gamma_{ij} \}_{0 \leq i +j \leq m}$ be a given
complex-valued sequence. The truncated complex moment problem (TCMP in short)
involves determining necessary and sufficient conditions for the existence of a
positive Borel measure $\mu$ on $\mathbb{C}$ (called a representing measure for
$\gamma^{(m)}$) such that $\gamma_{ij} = \int \overline{z}^i z^j d\mu$ for $0
\leq i +j \leq m$. The TCMP has been completely solved only when $m= 1, 2, 3,
4$.
  We provide in this paper a concrete solution to the quintic TCMP (that is,
when $m = 5$). We also study the cardinality of the minimal representing
measure. Based on the bivariate recurrences sequences's properties with some
Curto-Fialkow's results, our method intended to be useful for all odd-degree
moment problems.

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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th