The operator approach to the truncated multidimensional moment problem

Zagorodnyuk, Sergey M.

doi:10.1515/conop-2019-0001

Cited by 2 publications

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“…In general, the ideas of the operator approach to moment problems go back to the works of Naimark in 1940-1943 and then they were developed by many authors, see historical notes in [15]. In [17] we presented the operator approach to the truncated multidimensional moment problem in R n . Other approaches to truncated moment problems can be found in [4], [5], [13], [16], [9], [8].…”

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On the truncated multidimensional moment problems in $\mathbb{C}^n$

Zagorodnyuk

2021

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We consider the problem of finding a (non-negative) measureHere K is an arbitrary finite subset of Z n + , which contains (0, ..., 0), and s 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 R n , where the support of the measure µ is allowed to lie in C n . Secondly, the moment problem is a particular case of the truncated moment problem in 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.

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On the truncated multidimensional moment problems in $\mathbb{C}^n$

Zagorodnyuk

2021

Preprint

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On the Truncated Multidimensional Moment Problems in Cn

Zagorodnyuk

2022

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We consider the problem of finding a (non-negative) measure μ on B(Cn) such that ∫Cnzkdμ(z)=sk, ∀k∈K. Here, K is an arbitrary finite subset of Z+n, which contains (0,…,0), and sk are prescribed complex numbers (we use the usual notations for multi-indices). There are two possible interpretations of this problem. Firstly, one may consider this problem as an extension of the truncated multidimensional moment problem on Rn, where the support of the measure μ is allowed to lie in Cn. Secondly, the moment problem is a particular case of the truncated moment problem in Cn, 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.

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The operator approach to the truncated multidimensional moment problem

Cited by 2 publications

References 23 publications

On the truncated multidimensional moment problems in $\mathbb{C}^n$

On the truncated multidimensional moment problems in $\mathbb{C}^n$

On the Truncated Multidimensional Moment Problems in Cn

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