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• W3100563640 abstract "We show that the multivariate generating function of appropriately normalized moments of a measure with homogeneous polynomial density supported on a compact polytope P in R^d is a rational function. Its denominator is the product of linear forms dual to the vertices of P raised to the power equal to the degree of the density function. Using this, we solve the inverse moment problem for the set of, not necessarily convex, polytopes having a given set S of vertices. Under a weak non-degeneracy assumption we also show that the uniform measure supported on any such polytope is a linear combination of uniform measures supported on simplices with vertices in S." @default.
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• W3100563640 date "2018-04-12" @default.
• W3100563640 modified "2023-10-11" @default.
• W3100563640 title "On moments of a polytope" @default.
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• W3100563640 doi "https://doi.org/10.1007/s13324-018-0226-8" @default.
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