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• W2952344169 abstract "For a degree 2n real d-dimensional multisequence beta^(2n) to have a representing measure, it is necessary for the associated moment matrix M(n) to be positive semidefinite and for the algebraic variety V = V(beta) associated to beta to satisfy rank M(n) <= card V as well as the following consistency condition: if a polynomial p vanishes on V, then p(beta) = 0. We prove that for the extremal case (rank M(n) = card V), positivity of M(n) and consistency are sufficient for the existence of a (unique, rank M(n)-atomic) representing measure. We also show that in the preceding result, consistency cannot always be replaced by recursiveness of M(n)." @default.
• W2952344169 created "2019-06-27" @default.
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• W2952344169 date "2006-10-28" @default.
• W2952344169 modified "2023-09-27" @default.
• W2952344169 title "The extremal truncated moment problem" @default.
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