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- W2950992145 abstract "We employ positivity of Riesz functionals to establish representing measures (or approximate representing measures) for truncated multivariate moment sequences. For a truncated moment sequence $y$, we show that $y$ lies in the closure of truncated moment sequences admitting representing measures supported in a prescribed closed set $K subseteq re^n$ if and only if the associated Riesz functional $L_y$ is $K$-positive. For a determining set $K$, we prove that if $L_y$ is strictly $K$-positive, then $y$ admits a representing measure supported in $K$. As a consequence, we are able to solve the truncated $K$-moment problem of degree $k$ in the cases: (i) $(n,k)=(2,4)$ and $K=re^2$; (ii) $ngeq 1$, $k=2$, and $K$ is defined by one quadratic equality or inequality. In particular, these results solve the truncated moment problem in the remaining open cases of Hilbert's theorem on sums of squares." @default.
- W2950992145 created "2019-06-27" @default.
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- W2950992145 date "2009-08-22" @default.
- W2950992145 modified "2023-10-16" @default.
- W2950992145 title "Positivity of Riesz Functionals and Solutions of Quadratic and Quartic Moment Problems" @default.
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