Abstract
The main subject of this chapter and the next is the moment problem on closed semi-algebraic sets. For a compact semi-algebraic set \(\mathcal{K}(\mathsf{f})\) a very satisfactory solution of the existence problem in terms of the positivity on the preordering T(f) was given by Theorem 12.25. This result holds for any finite set f of generators which defines the semi-algebraic set \(\mathcal{K}(\mathsf{f})\). The representing measure is always unique and supported on \(\mathcal{K}(\mathsf{f})\). All these features of the compact case are no longer true for noncompact sets. In this chapter we are only concerned with existence problems, while determinacy questions are studied in the next chapter.
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Schmüdgen, K. (2017). The Moment Problem on Closed Semi-Algebraic Sets: Existence. In: The Moment Problem. Graduate Texts in Mathematics, vol 277. Springer, Cham. https://doi.org/10.1007/978-3-319-64546-9_13
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