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http://dx.doi.org/10.4134/CKMS.c180432

THE FLAT EXTENSION OF NONSINGULAR EMBRY MOMENT MATRICES E(3)  

Li, Chunji (Department of Mathematics Northeastern University)
Liang, Hongkai (Department of Mathematics Northeastern University)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.1, 2020 , pp. 137-149 More about this Journal
Abstract
Let γ(n) ≡ {γij} (0 ≤ i+j ≤ 2n, |i-j| ≤ n) be a sequence in the complex number set ℂ and let E (n) be the Embry truncated moment matrices corresponding from γ(n). For an odd number n, it is known that γ(n) has a rank E (n)-atomic representing measure if and only if E(n) ≥ 0 and E(n) admits a flat extension E(n + 1). In this paper we suggest a related problem: if E(n) is positive and nonsingular, does E(n) have a flat extension E(n + 1)? and give a negative answer in the case of E(3). And we obtain some necessary conditions for positive and nonsingular matrix E (3), and also its sufficient conditions.
Keywords
Embry truncated complex moment problem; representing measure; flat extension;
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Times Cited By KSCI : 2  (Citation Analysis)
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