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Sebestyén moment problem: The multi-dimensional case

Authors:	Dan Popovici Zoltá n Sebestyé n

Institution:	Department of Mathematics, University of the West, Ro-1900 Timisoara, Bd. V. Pârvan 4, Romania ; Department of Applied Analysis Loránd Eötvös University, H-1117 Budapest, Pázmány Péter sétány 1/C, Hungary

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 $\vert\Omega\vert=2$ .

Keywords:	Sebesty\'en operator moment problem multi-contraction regular dilation positive definite function

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