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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Sebestyén moment problem: The multi-dimensional case
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by Dan Popovici and Zoltán Sebestyén PDF
Proc. Amer. Math. Soc. 132 (2004), 1029-1035 Request permission

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{equation*} h_{\mathbf {n}}=\mathbf {T} ^{\mathbf {n}} h_{\mathbf {0}},\quad \mathbf {n}\in \mathbb {Z}_+^\Omega . \end{equation*} The theorem is a multi-dimensional analogue for some well-known operator moment problems due to Sebestyén in case $|\Omega |=1$ or, recently, to Găvruţă and Păunescu in case $|\Omega |=2$.
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Additional Information
  • Dan Popovici
  • Affiliation: Department of Mathematics, University of the West, Ro-1900 Timişoara, Bd. V. Pârvan 4, Romania
  • Email: popovici@math.uvt.ro
  • Zoltán Sebestyén
  • Affiliation: Department of Applied Analysis Loránd Eötvös University, H-1117 Budapest, Pázmány Péter sétány 1/C, Hungary
  • Email: sebesty@cs.elte.hu
  • Received by editor(s): October 22, 2002
  • Published electronically: December 1, 2003

  • Dedicated: To the memory of Gyula Farkas
  • Communicated by: Joseph A. Ball
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 1029-1035
  • MSC (2000): Primary 47A57, 47A20
  • DOI: https://doi.org/10.1090/S0002-9939-03-07291-5
  • MathSciNet review: 2045418