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- Title
Charges solve the truncated complex moment problem.
- Authors
Idrissi, K.; Zerouali, E. H.
- Abstract
Let γ ≡ { γ i j } (i , j) ∈ I , with I ⊆ ℤ + × ℤ + and γ i j ¯ = γ j i , be a given complex-valued sequence. The complex moment problem (respectively, the general complex moment problem) associated with γ consists in determining necessary and sufficient conditions for the existence of a positive Borel measure (respectively, a charge) μ on ℂ such that γ i j = ∫ ℂ z ¯ i z j d μ , for (i , j) ∈ I. In this paper, we investigate the notion of recursiveness in the two variable case. We obtain several useful results that we use to deduce new necessary and sufficient conditions for the truncated complex moment problem to admit a solution. In particular, we show that the general complex moment problem always has a solution. A concrete construction of the solution and an illustrating example are also given.
- Subjects
BOREL subgroups; MOMENT problems (Mathematics); MATHEMATICAL sequences; PROBLEM solving; POLYNOMIALS
- Publication
Infinite Dimensional Analysis, Quantum Probability & Related Topics, 2018, Vol 21, Issue 4, pN.PAG
- ISSN
0219-0257
- Publication type
Article
- DOI
10.1142/S0219025718500273