A Note on The Multidimensional Moment Problem
Liqun Qi
TL;DR
This paper demonstrates that a multidimensional sequence forming Hankel tensors with all positive semi-definite Hankel matrices is a multidimensional moment sequence, linking tensor structures to moment problems.
Contribution
It establishes a new criterion connecting Hankel tensors and positive semi-definite Hankel matrices to multidimensional moment sequences.
Findings
Hankel tensors are linked to multidimensional moment sequences.
Positive semi-definiteness of Hankel matrices implies the sequence is a moment sequence.
Provides a theoretical criterion for multidimensional moment problems.
Abstract
In this note, we show that if a multidimensional sequence generates Hankel tensors and all the Hankel matrices, generated by this sequence, are positive semi-definite, then this sequence is a multidimensional moment sequence.
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Taxonomy
TopicsTensor decomposition and applications · Matrix Theory and Algorithms · Mathematical Approximation and Integration