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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
고응일scopus
Issue Date
2003
Journal Title
Linear Algebra and Its Applications
ISSN
0024-3795JCR Link
Citation
vol. 375, no. 1-3, pp. 95 - 114
Indexed
SCI; SCIE; SCOPUS WOS scopus
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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