By considering a bridge between Bram-Halmos and Embry characterizations for the subnormality of cyclic operators, we extend the Curto-Fialkow and Embry truncated complex moment problem, and solve the problem finding the finitely atomic representing measure $mu $ such that $gamma _{ij}=int ar{z}% ^{i}z^{j}dmu $, $(0leq i+jleq 2n$, $|i-j|leq n+s,$ $0leq sleq n);$ the cases of $s=n$ and $s=0$ are induced by Bram-Halmos and Embry characterizations, respectively. The former is the Curto-Fialkow truncated complex moment problem and the latter is the Embry truncated complex moment problem.
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机译：通过考虑Bram-Halmos和Embry刻画之间的桥梁来解决循环算子的次正规性，我们扩展了Curto-Fialkow和Embry截断的复矩问题，并解决了发现有限原子表示度量$ mu $这样的问题，即$ gamma的问题。 _ {ij} = int bar {z}％^ {i} z ^ {j} d mu $，$（0 leq i + j leq 2n $，$ | ij | leq n + s， $ $ 0 leq s leq n）; $ s = n $和$ s = 0 $的情况分别由Bram-Halmos和Embry表征引起。前者是Curto-Fialkow截断的复杂矩问题，后者是Embry截断的复杂矩问题。
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