Pushforwards of Lebesgue measure restricted to convex d-polytopes onto a line produce spline densities whose moments obey higher Prony systems, with the directional moment variety identified as the Hankel determinantal variety from moment varieties of measures on polytopes.
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Projections of convex polytopes to a line and higher univariate Prony systems
Pushforwards of Lebesgue measure restricted to convex d-polytopes onto a line produce spline densities whose moments obey higher Prony systems, with the directional moment variety identified as the Hankel determinantal variety from moment varieties of measures on polytopes.