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Finite-Dimensional Completion for the Matrix-Valued Truncated Complex Moment Problem

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Abstract

In this paper, we consider the matrix-valued truncated complex moment problem. We notice first that if a truncated complex matrix-valued sequence admits a representing measure, then it is the initial data of an infinite complex matrix-valued sequence verifying some suitable finite-dimensional property. We show that finite-dimensional completion of a truncated data provides a necessary and sufficient condition, and hence a solution, for the matrix-valued truncated complex moment problem. As a consequence, we obtain a matrix generalization of Curto–Fialkow’s result on flat positive extensions of moment matrices.

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Funding

The authors are supported by the Centre of Mathematical Research in Rabat. The last author is supported by African University of Sciences and Technology-Abuja, Nigeria.

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  1. Laboratory of Mathematic Analysis and Applications, Faculty of SciencesMohammed V University in Rabat, Rabat, Morocco

    Kaissar Idrissi, Imane Naainia & El Hassan Zerouali

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  1. Kaissar Idrissi
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  2. Imane Naainia
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  3. El Hassan Zerouali
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Correspondence to Kaissar Idrissi.

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Idrissi, K., Naainia, I. & Zerouali, E.H. Finite-Dimensional Completion for the Matrix-Valued Truncated Complex Moment Problem. Results Math 78, 84 (2023). https://doi.org/10.1007/s00025-023-01851-4

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