Boris Shapiro: On moments of a polytope
Boris Shapiro, SU
Tid: On 2012-09-12 kl 13.15 - 14.15
Plats: Room 3721, Lindstedtsvägen 25, 7th floor, Department of Mathematics, KTH
We show that a multivariate generating function of appropriately normalized moments of an arbitrary compact polytope P in R^d with respect to an arbitrary homogeneous polynomial weight function 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 weight function. (The used normalization of moments is connected with a special case of the Fantappiè transform of the weight studied in the 80s by late M.Passare). Using this approach we solve the inverse moment problem for the set of polytopes having a given fixed set of vertices. Some unexpected consequences for the theory of polytopes will be given.
This project was carried out jointly with N.Gravin, D. Pasechnik (NTU-SIngapore) and M. Shapiro (Michigan State).