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Measures with zeros in the inverse of their moment matrix. (English) Zbl 1169.15005

The paper focuses on the multivariate truncated moment matrix, \(M_d\), consisting of moments of a measure \(\mu\) up to an order determined by \(d\). First, the authors describe precisely which pattern of zeros of \(M_d^{-1}\) corresponds to independence, namely, the measure \(\mu\) having a product type structure. Next, the authors turn to the study of a particular entry of \(M_d^{-1}\) being zero. They find that the key factor is a certain conditional triangularity property of the orthogonal polynomials up to degree \(2d\), associated with the measure \(\mu\).

MSC:

15B51 Stochastic matrices
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis

References:

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