@article{Marshall_2014, title={Application of Localization to the Multivariate Moment Problem}, volume={115}, url={https://www.mscand.dk/article/view/19225}, DOI={10.7146/math.scand.a-19225}, abstractNote={It is explained how the localization technique introduced by the author in [19] leads to a useful reformulation of the multivariate moment problem in terms of extension of positive semidefinite linear functionals to positive semidefinite linear functionals on the localization of $\mathsf{R}[\underline{x}]$ at $p = \prod_{i=1}^n(1+x_i^2)$ or $p’ = \prod_{i=1}^{n-1}(1+x_i^2)$. It is explained how this reformulation can be exploited to prove new results concerning existence and uniqueness of the measure $\mu$ and density of $\mathsf{C}[\underline{x}]$ in $\mathscr{L}^s(\mu)$ and, at the same time, to give new proofs of old results of Fuglede [11], Nussbaum [21], Petersen [22] and Schmüdgen [27], results which were proved previously using the theory of strongly commuting self-adjoint operators on Hilbert space. }, number={2}, journal={MATHEMATICA SCANDINAVICA}, author={Marshall, Murray}, year={2014}, month={Dec.}, pages={269–286} }