论文标题
索引集中截断的汉堡瞬间问题
The truncated Hamburger moment problems with gaps in the index set
论文作者
论文摘要
在本文中，我们解决了$ 2K $ $ 2K $的截短汉堡瞬间问题（THMP）的四个特殊案例，序列中有一个或两个缺失的时刻。作为推论，我们通过使用适当的替换获得了特殊曲线的两种截短力矩问题$ 2K $的解决方案。也就是说，对于曲线，$ y = x^3 $（首先由fialkow求解），$ y^2 = x^3 $，$ y = x^4 $，其中一定程度的$ 2K+1 $，$ y^3 = x^4 $，带有某个时刻。主要技术是部分阳性半芬酸盐基质（PPSD）的完成，使Curto和Fialkow的THMP解决方案的条件得到满足。主要工具是使用正式半金融矩阵的属性，以及所有完整的PPSD矩阵的结果，其中一个未知条目，这是通过使用Schur补语以$ 2 \ times 2 $ 2 $和$ 3 \ times 3 $ 3 $ 3 $块矩阵证明的。
In this article we solve four special cases of the truncated Hamburger moment problem (THMP) of degree $2k$ with one or two missing moments in the sequence. As corollaries we obtain, by using appropriate substitutions, the solutions to bivariate truncated moment problems of degree $2k$ for special curves. Namely, for the curves $y=x^3$ (first solved by Fialkow), $y^2=x^3$, $y=x^4$ where a certain moment of degree $2k+1$ is known and $y^3=x^4$ with a certain moment given. The main technique is the completion of the partial positive semidefinite matrix (ppsd) such that the conditions of Curto and Fialkow's solution of the THMP are satisfied. The main tools are the use of the properties of positive semidefinite Hankel matrices and a result on all completions of a ppsd matrix with one unknown entry, proved by the use of the Schur complements for $2\times 2$ and $3\times 3$ block matrices.
