Journal article
Truncated K-moment problems in several variables
Journal of operator theory, Vol.54(1), pp.189-226
06/01/2005
Abstract
dLet beta - beta((2n)) be an N-dimensional real multi-sequence of degree 2n, with associated moment matrix M(n) equivalent to M(n)(beta), and let r := rank M(n). We prove that if M(n) is positive semidefinite and admits a rank-preserving moment matrix extension M(n + 1), then M(n + 1) has a unique representing measure mu, which is r-atomic, with supp mu equal to V (M(n + 1)), the algebraic variety of M(n + 1). Further, P has an r-atomic (minimal) representing measure supported in a semi-algebraic set K-Q subordinate to a family Q equivalent to {q(i)}(i=1)(m) subset of R[t(1),..., t(N)] if and only if M(n) is positive semidefinite and admits a rank-preserving extension M(n + 1) for which the associated localizing matrices M-qi(n + [1+gegq(i)/2]) are positive semidefinite, 1 <= i <= m; in this case, It (as above) satisfies supp mu subset of K-Q, and mu has precisely rank M(n) - rank M-qi (n + [1+degq(i)/2]) atoms in Z(q(i)) equivalent to {t is an element of R-N:q(i)(t) = 0}, 1 <= i <= m.
Details
- Title: Subtitle
- Truncated K-moment problems in several variables
- Creators
- R E CurtoL A Fialkow
- Resource Type
- Journal article
- Publication Details
- Journal of operator theory, Vol.54(1), pp.189-226
- Publisher
- THETA FOUNDATION
- ISSN
- 0379-4024
- eISSN
- 1841-7744
- Number of pages
- 38
- Language
- English
- Date published
- 06/01/2005
- Academic Unit
- Mathematics
- Record Identifier
- 9984240861702771
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