Advances in Operator Theory

On the truncated two-dimensional moment problem

Sergey Zagorodnyuk

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We study the truncated two-dimensional moment problem (with rectangular data) to find a non-negative measure $\mu(\delta)$, $\delta\in\mathfrak{B}(\mathbb{R}^2)$, such that $\int_{\mathbb{R}^2} x_1^m x_2^n d \mu = s_{m,n}$, $0\leq m\leq M,\quad 0\leq n\leq N$, where $\{ s_{m,n} \}_{0\leq m\leq M, 0\leq n\leq N}$ is a prescribed sequence of real numbers; $M,N\in\mathbb{Z}_+$. For the cases $M=N=1$ and $M=1, N=2$ explicit numerical necessary and sufficient conditions for the solvability of the moment problem are given. In the cases $M=N=2$; $M=2, N=3$; $M=3, N=2$; $M=3, N=3$ some explicit numerical sufficient conditions for the solvability are obtained. In all the cases some solutions (not necessarily atomic) of the moment problem can be constructed.

Article information

Adv. Oper. Theory Volume 3, Number 2 (2018), 388-399.

Received: 4 August 2017
Accepted: 22 October 2017
First available in Project Euclid: 15 December 2017

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Digital Object Identifier

Primary: 47A57: Operator methods in interpolation, moment and extension problems [See also 30E05, 42A70, 42A82, 44A60]
Secondary: 44A60: Moment problems

Hankel matrix moment problem non-linear inequalities


Zagorodnyuk, Sergey. On the truncated two-dimensional moment problem. Adv. Oper. Theory 3 (2018), no. 2, 388--399. doi:10.15352/AOT.1708-1212.

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