Embry truncated complex moment problem.
type: Item
instance of: scholarly article
title: Embry truncated complex moment problem.
zbMATH Open document ID: 1048.44001
DOI: 10.1016/S0024-3795(03)00617-7
author: Il Bong Jung
author: Eungil Ko
author: Chunji Li
author: Sang Soo Park
published in: Linear Algebra and its Applications
publication date: 2003-12-04T00:00:00Z
review text: The truncated complex moment problem consists in the following: given a collection of complex numbers \(\{\gamma_{ij}\}\) \((0\leq i+j\leq n)\), find a positive Borel measure \(\mu\) on \({\mathbb C}\) such that \(\gamma_{ij}=\int\bar z^iz^j \,d\mu(z)\). A criterion for solvability the truncated complex moment problem was given by \textit{R. Curto} and \textit{L. Fialkow} [Mem. Am. Math. Soc. 648 (1998; Zbl 0913.47016)] in terms of the corresponding moment matrix \(M(n)\). The authors consider the truncated complex moment problem with the moments \(\gamma_{ij}\) subject to the following restrictions \(0\leq i+j\leq n\), \(| i-j| \leq n\) and give a solvability criterion in terms of a submatrix \(E(n)\) of the matrix \(M(n)\). The proof is based on a generalization of the Halmos-Bram criterion for subnormality found by \textit{M. Embry} [Acta Sci. Math. 35, 61--64 (1973; Zbl 0263.47023)].
reviewed by: V. A. Derkach
Mathematics Subject Classification ID: 44A60
Mathematics Subject Classification ID: 47B20
zbMATH DE Number: 2013046
zbMATH Keywords: truncated complex moment problem
zbMATH Keywords: subnormal operators
zbMATH Keywords: k-hyponormal operators
describes a project that uses: Mathematica
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2013046