论文标题
在最小的解决方案上，无限期截短的多维矩问题
On a minimal solution for the indefinite truncated multidimensional moment problem
论文作者
论文摘要
我们将考虑无限期的截短多维矩问题。 Necessary and sufficient conditions for a given truncated multisequence to have a signed representing measure $μ$ with ${\rm card}\,{\rm supp}\, μ$ as small as possible are given by the existence of a rank preserving extension of a multivariate Hankel matrix (built from the given truncated multisequence) such that the corresponding associated polynomial ideal is real radical.该结果是一种特殊情况，它是对截断的多质量的更一般性表征，具有最小的复合物，代表其支持相对于复杂的共轭对称的措施（我们将其称为{\ it quasi-complex}）。我们结果的一个动机是一个事实，即积极的半决赛截短多次数不必具有积极的代表度量。因此，我们的主要结果赋予了计算签名的表示度量$μ=μ_+-μ_- $的潜力，其中$ {\ rm card} \，μ_- $很小。我们在具体示例上说明了这一点。
We will consider the indefinite truncated multidimensional moment problem. Necessary and sufficient conditions for a given truncated multisequence to have a signed representing measure $μ$ with ${\rm card}\,{\rm supp}\, μ$ as small as possible are given by the existence of a rank preserving extension of a multivariate Hankel matrix (built from the given truncated multisequence) such that the corresponding associated polynomial ideal is real radical. This result is a special case of a more general characterisation of truncated multisequences with a minimal complex representing measure whose support is symmetric with respect to complex conjugation (which we will call {\it quasi-complex}). One motivation for our results is the fact that positive semidefinite truncated multisequence need not have a positive representing measure. Thus, our main result gives the potential for computing a signed representing measure $μ= μ_+ - μ_-$, where ${\rm card} \,μ_-$ is small. We illustrate this point on concrete examples.
