The extremal truncated moment problem
Functional Analysis
2007-05-23 v1 Algebraic Geometry
Operator Algebras
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).
Keywords
Cite
@article{arxiv.math/0610882,
title = {The extremal truncated moment problem},
author = {Raul E. Curto and Lawrence A. Fialkow and H. Michael Moeller},
journal= {arXiv preprint arXiv:math/0610882},
year = {2007}
}