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arXiv · 1805.12060

On the Uniqueness Result of Theorem 6 in "Relative Entropy and the Multivariable Multidimensional Moment Problem"

Bin Zhu
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Abstract

Matrix-valued covariance extension and multivariate spectral estimation are formulated as generalized moment problems in the "THREE" approach and its extensions. Under this context, we discuss Theorem 6 in \cite{Georgiou-06} concerning the bijectivity of a moment map defined over a parametric family of spectral densities. In particular, we provide a counterexample in which the moment map under consideration is shown to have a critical point, namely a point at which the Jacobian loses rank. Then with standard techniques in bifurcation theory, we conclude further that the computed critical point is a bifurcation point, which means that the moment map is not injective.

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Bin Zhu. 2018-05-30. On the Uniqueness Result of Theorem 6 in "Relative Entropy and the Multivariable Multidimensional Moment Problem". https://doi.org/10.1109/tit.2019.2903129

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