• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.949-970
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• 2007

By considering a bridge between Bram-Halmos and Embry characterizations for the subnormality of cyclic operators, we extend the Curto-Fialkow and Embry truncated complex moment problem, and solve the problem finding the finitely atomic representing measure ${\mu}$ such that ${\gamma}_{ij}={\int}\bar{z}^iz^jd{\mu},\;(0{\le}i+j{\le}2n,\;|i-j|{\le}n+s,\;0{\le}s{\le}n);$ the cases of s = n and s = 0 are induced by Bram-Halmos and Embry characterizations, respectively. The former is the Curto-Fialkow truncated complex moment problem and the latter is the Embry truncated complex moment problem.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.337-350
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• 2007

Given a collection of complex numbers ${\gamma}{\equiv}\{{\gamma}ij\}$ $(0{\leq}i+j{\leq}2n,\;|i-j|{\leq}n)$ with ${\gamma}00>0\;and\;{\gamma}ji=\bar{\gamma}ij$, we consider the moment problem for ${\gamma}$ in the case of n=2, which is referred to Embry quartic moment problem. In this note we give a partial solution for the nonsingular case of Embry quartic moment problem.

• Communications of the Korean Mathematical Society
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• v.21 no.3
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• pp.433-449
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• 2006

In this paper, we present some recent developments on hyponormal operator theory and truncated Curto-Fialkow and Embry complex moment problems.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.137-149
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• 2020

Let γ⁽ⁿ⁾ ≡ {γ_ij} (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.