Measures with zeros in the inverse of their moment matrix

J.W. Helton(heltonmath.ucsd.edu)
J.B. Lasserre(lasserrelaas.fr)
M. Putinar(mputinarmath.ucsb.edu)

Abstract: We investigate and discuss when the inverse of a multivariate truncated moment matrix of a measure 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 the measure.

Keywords: Moment matrix; orthogonal polynomials

Category 1: Applications -- Science and Engineering (Statistics )

Category 2: Other Topics (Other )

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Entry Submitted: 02/14/2007
Entry Accepted: 02/14/2007
Entry Last Modified: 02/14/2007

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