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Spring 2018 On the truncated two-dimensional moment problem
Sergey Zagorodnyuk
Adv. Oper. Theory 3(2): 388-399 (Spring 2018). DOI: 10.15352/AOT.1708-1212

Abstract

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.

Citation

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Sergey Zagorodnyuk. "On the truncated two-dimensional moment problem." Adv. Oper. Theory 3 (2) 388 - 399, Spring 2018. https://doi.org/10.15352/AOT.1708-1212

Information

Received: 4 August 2017; Accepted: 22 October 2017; Published: Spring 2018
First available in Project Euclid: 15 December 2017

zbMATH: 06848507
MathSciNet: MR3738219
Digital Object Identifier: 10.15352/AOT.1708-1212

Subjects:
Primary: 47A57
Secondary: 44A60

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.3 • No. 2 • Spring 2018
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