A functional characterization of certain mixed volumes |
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Authors: | William J Firey |
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Institution: | (1) Mathematics Department, Oregon State University, 97331 Corvallis, Oregon, USA |
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Abstract: | A function over the convex coneK{inn}, of convex bodiesK in Euclideann-space (where addition is vector addition, positive scalar multiplication is dilatation), which is linear overK{inn}, increasing with respect to set inclusion, and zero at point bodies must be a mixed volumeV(K; đ, p−1;σ
1, …,σ
n−p). Heređ, takenp−1 times, is inK{inn} andσ
1, …,σ
n−pare pairwise orthogonal unit segments spanning the orthogonal complement of the affine hull ofđ. |
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Keywords: | |
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