The Moment Problem with Bounded Density
نویسنده
چکیده
Let μ be a given Borel measure on K ⊆ R and let y = (yα), α ∈ N, be a given sequence. We provide several conditions linking y and the moment sequence z = (zα) of μ, for y to be the moment sequence of a Borel measure ν on K which is absolutely continuous with respect to μ and such that its density is in L∞(K, μ). The conditions are necessary and sufficient if K is a compact basic semi-algebraic set, and sufficient if K ≡ R. Moreover, arbitrary finitely many of these conditions can be checked by solving either a semidefinite program or a linear program with a single variable!
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