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Embry truncated complex moment problem
- Title
- Embry truncated complex moment problem
- Authors
- Jung I.B.; Ko E.; Li C.; Park S.S.
- Ewha Authors
- 고응일
- SCOPUS Author ID
- 고응일
- Issue Date
- 2003
- Journal Title
- Linear Algebra and Its Applications
- ISSN
- 0024-3795
- Citation
- Linear Algebra and Its Applications vol. 375, no. 1-3, pp. 95 - 114
- Indexed
- SCI; SCIE; SCOPUS
- Document Type
- Article
- Abstract
- Let T be a cyclic subnormal operator on a Hilbert space ℋ with cyclic vector x0 and let γij:=(T*iT jx0,x0), for any i,j ∈ ℕ ∪ {0}. The Bram-Halmos' characterization for subnormality of T involved a moment matrix M(n). In a parallel approach, we construct a moment matrix E(n) corresponding to Embry's characterization for subnormality of T. We discuss the relationship between M(n) and E(n) via the full moment problem. Next, given a collection of complex numbers γ≡{γij} (0 ≤ i + j ≤ 2n, |i-j| ≤ n) with γ00 > 0 and γ ji = γ̄ij, we consider the truncated complex moment problem for γ; this entails finding a positive Borel measure μ supported in the complex plane ℂ such that γij = ∫z̄izjdμ(z). We show that this moment problem can be solved when E(n) ≥ 0 and E(n) admits a flat extension E(n + k), where k = 1 when n is odd and k = 2 when n is even. © 2003 Elsevier Inc. All rights reserved.
- DOI
- 10.1016/S0024-3795(03)00617-7
- Appears in Collections:
- 자연과학대학 > 수학전공 > Journal papers
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