Zonoids and Conditionally Positive Definite Functions

Markus Burger

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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