Abstract
The fibre theorem [12] for the moment problem on closed semi-algebraic subsets of Rd is generalized to finitely generated real unital algebras. As an application two new theorems on the rational multidimensional moment problem are proved. Another application is a characterization of moment functionals on the polynomial algebra R[x 1,..., x d ] in terms of extensions. Finally, the fibre theorem and the extension theorem are used to reprove basic results on the complex moment problem due to Stochel and Szafraniec [13] and Bisgaard [2].
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Dedicated to the memory of Murray Marshall (1940–2015)
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Schmüdgen, K. A general fibre theorem for moment problems and some applications. Isr. J. Math. 218, 43–66 (2017). https://doi.org/10.1007/s11856-017-1458-2
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DOI: https://doi.org/10.1007/s11856-017-1458-2