Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 57, No. 4, pp. 443-458 (2000)

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Zonoids and Conditionally Positive Definite Functions

Markus Burger

Mathematisches Institut II, Universität Karlsruhe,
D-76128 Karlsruhe - GERMANY

Abstract: It is well-known in convex geometry that a centrally symmetric convex body $Z\subset\R^d$ is a zonoid (a limit of sums of line segments), if and only if its support function $h$ has the property that -$h$ is conditionally positive definite. Here, we give a new proof of this result using extreme point methods.

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Electronic version published on: 31 Jan 2003. This page was last modified: 27 Nov 2007.

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