Measures with zeros in the inverse of their moment matrix
Helton, J. William ; Lasserre, Jean B. ; Putinar, Mihai
Ann. Probab., Tome 36 (2008) no. 1, p. 1453-1471 / Harvested from Project Euclid
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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.
Publié le : 2008-07-15
Classification:  Moment matrix,  orthogonal polynomials,  52A20,  52A 
@article{1217360975,
     author = {Helton, J. William and Lasserre, Jean B. and Putinar, Mihai},
     title = {Measures with zeros in the inverse of their moment matrix},
     journal = {Ann. Probab.},
     volume = {36},
     number = {1},
     year = {2008},
     pages = { 1453-1471},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1217360975}
}

Helton, J. William; Lasserre, Jean B.; Putinar, Mihai. Measures with zeros in the inverse of their moment matrix. Ann. Probab., Tome 36 (2008) no. 1, pp.  1453-1471. http://gdmltest.u-ga.fr/item/1217360975/