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Radial continuous rotation invariant valuations on star bodies

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Villanueva, Ignacio (2016) Radial continuous rotation invariant valuations on star bodies. Advances in Mathematics, 291 (19). pp. 961-981. ISSN 0001-8708

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Official URL: http://www.sciencedirect.com/science/article/pii/S0001870816000335




Abstract

We characterize the positive radial continuous and rotation invariant valuations V defined on the star bodies of Rn as the applications on star bodies which admit an integral representation with respect to the Lebesgue measure. That is,V(K)=∫Sn−1θ(ρK)dm, where θ is a positive continuous function, ρK is the radial function associated to K and m is the Lebesgue measure on Sn−1. As a corollary, we obtain that every such valuation can be uniformly approximated on bounded sets by a linear combination of dual quermassintegrals.


Item Type:Article
Uncontrolled Keywords:Convex geometry; Valuations; Star bodies
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:36032
Deposited On:02 Mar 2016 10:03
Last Modified:04 Apr 2016 10:04

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