On moments of a polytope
We show that the multivariate generating function of appropriately normalized moments of a measure with homogeneous polynomial density supported on a compact polytope P⊂Rd is a rational function. Its denominator is the product of linear forms dual to the vertices of P raised to the power equal...
| Main Authors: | , , , |
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| Format: | Journal article |
| Published: |
Springer Verlag
2018
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| Summary: | We show that the multivariate generating function of appropriately normalized moments of a measure with homogeneous polynomial density supported on a compact polytope P⊂Rd 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. |
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