bibkey: schmudgen2020moment authors: Konrad Schmüdgen year: 2020 title: “Ten Lectures on the Moment Problem” doi: null url: https://arxiv.org/abs/2008.12698v1 claim: “Compact truncated moment positivity and moment-matrix kernels give support restrictions through nonnegative polynomials of zero integral.” strata_touched: [] license: citation-only triage: anchor

Support certificates from truncated observations

Source: https://arxiv.org/abs/2008.12698v1. Lecture 3, Theorems 3.1 and 3.2, PDF p. 24, gives the even and odd truncated $[a,b]$ moment criteria. Lecture 9, Proposition 9.2(i), (ii), (iv), (v), PDF p. 68, identifies $L(fg)$ with the moment-matrix quadratic form and puts every representing measure on the zero sets of its kernel polynomials.

LocalClock, §十四, 定理27 consumes $L(P^2)=0\Rightarrow \mathrm{supp}\nu \subseteq \{P=0\}$ to constrain the actual five-mode source. The measure there is already supplied, so no claim that arbitrary positive semidefinite truncated Hankel data alone represent a measure on $[0,1]$ is needed. For reconstruction from putative data, the interval-localizing conditions in Theorems 3.1 and 3.2 must also be retained.

Nonzero $P$ is required to deduce finite support in one variable. Approximate residuals give the consumer’s stated concentration and finite-time moment error, not exact support. No general flat-extension or full Borel-flow rigidity result is attributed to this scalar application.