Minkowski valuations on 𝐿^{𝑝}-spaces

Tsang, Andy

doi:10.1090/S0002-9947-2012-05681-9

Minkowski valuations on $L^p$-spaces
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Trans. Amer. Math. Soc. 364 (2012), 6159-6186 Request permission

Abstract:

A complete classification is obtained of continuous $\operatorname {GL}(n)$- equivariant Minkowski valuations on $L^p(\mathbb {R}^n,|x|dx)$. As a consequence, a characterization of the moment body for functions is obtained.

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