The extremal truncated moment problem
| dc.creator | Curto, Raul E. | |
| dc.creator | Fialkow, Lawrence A. | |
| dc.creator | Moeller, H. Michael | |
| dc.date | 2006-10-28 | |
| dc.date.accessioned | 2026-07-07T07:29:34Z | |
| dc.date.available | 2026-07-07T07:29:34Z | |
| dc.description | For a degree 2n real d-dimensional multisequence β^(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(β) associated to βto satisfy rank M(n) <= card V as well as the following consistency condition: if a polynomial p vanishes on V, then p(β) = 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). | |
| dc.identifier | https://arxiv.org/abs/math/0610882 | |
| dc.identifier | http://arxiv.org/abs/math/0610882 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/118159 | |
| dc.subject | Functional Analysis | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Operator Algebras | |
| dc.subject | 47A57; 44A60; 42A70; 30A05 | |
| dc.title | The extremal truncated moment problem | |
| dc.type | text |