Lebesgue decomposition in action via semidefinite relaxations |
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Authors: | Jean B Lasserre |
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Institution: | 1.LAAS-CNRS and Institute of Mathematics,University of Toulouse, LAAS,Toulouse,France |
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Abstract: | Given all (finite) moments of two measures μ and λ on \(\mathbb {R}^{n}\), we provide a numerical scheme to obtain the Lebesgue decomposition μ = ν + ψ with ν?λ and ψ ⊥ λ. When ν has a density in \(L_{\infty }(\lambda )\) then we obtain two sequences of finite moments vectors of increasing size (the number of moments) which converge to the moments of ν and ψ respectively, as the number of moments increases. Importantly, no à priori knowledge on the supports of μ,ν and ψ is required. |
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