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Measures with zeros in the inverse of their moment matrix

J. William Helton·Jean B. Lasserre·Mihai Putinar
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Abstract

We investigate and discuss when the inverse of a multivariate truncated moment matrix of a measure $μ$ has zeros in some prescribed entries. We describe precisely which pattern of these zeroes corresponds to independence, namely, the measure having a product structure. A more refined finding is that the key factor forcing a zero entry in this inverse matrix is a certain conditional triangularity property of the orthogonal polynomials associated with $μ$.

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J. William Helton, Jean B. Lasserre, Mihai Putinar. 2008-08-27. Measures with zeros in the inverse of their moment matrix. https://doi.org/10.1214/07-aop365

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