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Sebestyén moment problem: The multi-dimensional case

Authors: Dan Popovici and Zoltán Sebestyén
Journal: Proc. Amer. Math. Soc. 132 (2004), 1029-1035
MSC (2000): Primary 47A57, 47A20
Published electronically: December 1, 2003
MathSciNet review: 2045418
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Abstract: Given a family $\{h_{\mathbf{n}}\}_{\mathbf{n}\in\mathbb{Z} _+^\Omega}$ of vectors in a Hilbert space $\mathcal{H}$ we characterize the existence of a family of commuting contractions $\mathbf{T}=\{T_\omega\}_{w\in \Omega}$ on $\mathcal{H}$ having regular dilation and such that

\begin{displaymath}h_{\mathbf{n}}=\mathbf{T} ^{\mathbf{n}} h_{\mathbf{0}},\quad \mathbf{n}\in\mathbb{Z} _+^\Omega. \end{displaymath}

The theorem is a multi-dimensional analogue for some well-known operator moment problems due to Sebestyén in case $\vert\Omega\vert=1$ or, recently, to Gavruta and Paunescu in case $\vert\Omega\vert=2$.

References [Enhancements On Off] (What's this?)

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Additional Information

Dan Popovici
Affiliation: Department of Mathematics, University of the West, Ro-1900 Timişoara, Bd. V. Pârvan 4, Romania

Zoltán Sebestyén
Affiliation: Department of Applied Analysis Loránd Eötvös University, H-1117 Budapest, Pázmány Péter sétány 1/C, Hungary

Keywords: Sebesty\'en operator moment problem, multi-contraction, regular dilation, positive definite function
Received by editor(s): October 22, 2002
Published electronically: December 1, 2003
Dedicated: To the memory of Gyula Farkas
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society