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- W3129086225 abstract "We consider the problem of finding a (non-negative) measure $mu$ on $mathfrak{B}(mathbb{C}^n)$ such that $int_{mathbb{C}^n} mathbf{z}^{mathbf{k}} dmu(mathbf{z}) = s_{mathbf{k}}$, $forall mathbf{k}inmathcal{K}$. Here $mathcal{K}$ is an arbitrary finite subset of $mathbb{Z}^n_+$, which contains $(0,...,0)$, and $s_{mathbf{k}}$ are prescribed complex numbers (we use the usual notations for multi-indices). There are two possible interpretations of this problem. At first, one may consider this problem as an extension of the truncated multidimensional moment problem on $mathbb{R}^n$, where the support of the measure $mu$ is allowed to lie in $mathbb{C}^n$. Secondly, the moment problem is a particular case of the truncated moment problem in $mathbb{C}^n$, with special truncations. We give simple conditions for the solvability of the above moment problem. As a corollary, we have an integral representation with a non-negative measure for linear functionals on some linear subspaces of polynomials." @default.
- W3129086225 created "2021-02-15" @default.
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- W3129086225 date "2021-02-08" @default.
- W3129086225 modified "2023-09-26" @default.
- W3129086225 title "On the truncated multidimensional moment problems in $mathbb{C}^n$" @default.
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