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Journal article
THE TRUNCATED MATRIX-VALUED K-MOMENT PROBLEM ON R-d, C-d, AND T-d
Transactions of the American Mathematical Society, v 365(10), pp 5393-5430
01 Oct 2013
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Abstract
The truncated matrix-valued K-moment problem on R-d, C-d, and T-d will be considered. The truncated matrix-valued K-moment problem on Rd requires necessary and sufficient conditions for a multisequence of Hermitian matrices {S gamma}(gamma is an element of Gamma) (where Gamma is a finite subset of N-0(d)) to be the corresponding moments of a positive Hermitian matrix-valued Borel measure sigma, and also the support of sigma must be contained in some given non-empty set K subset of R-d, i. e.,
(0.1) S-gamma = integral(Rd) xi(gamma)d sigma(epsilon), for all gamma is an element of Gamma,
and
(0.2) supp sigma subset of K.
Given a non-empty set K subset of R-d and a finite multisequence, indexed by a certain family of finite subsets of N-0(d), of Hermitian matrices we obtain necessary and sufficient conditions for the existence of a minimal finitely atomic measure which satisfies (0.1) and (0.2). In particular, our result can handle the case when Gamma = {gamma is an element of N-0(d) : 0 <= |gamma| <= 2n + 1}. We will also discuss a similar result in the multivariable complex and polytorus setting.
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Details
- Title
- THE TRUNCATED MATRIX-VALUED K-MOMENT PROBLEM ON R-d, C-d, AND T-d
- Creators
- David P. Kimsey - Drexel UniversityHugo J. Woerdeman - Drexel University
- Publication Details
- Transactions of the American Mathematical Society, v 365(10), pp 5393-5430
- Publisher
- Amer Mathematical Soc
- Number of pages
- 38
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000326590600014
- Scopus ID
- 2-s2.0-84880388058
- Other Identifier
- 991019169913204721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics