Characterization of dual mixed volumes via polymeasures

TL;DR

This paper characterizes dual mixed volumes through functional properties of associated polynomials, employing multilinear operator theory on continuous function spaces, and rederives recent characterizations using these methods.

Contribution

It introduces a new functional characterization of dual mixed volumes and applies multilinear operator techniques to reprove existing results.

Findings

New functional characterization of dual mixed volumes

Application of multilinear operator theory to convex geometry

Reproof of recent dual mixed volume characterization

Abstract

We prove a characterization of the dual mixed volume in terms of functional properties of the polynomial associated to it. To do this, we use tools from the theory of multilinear operators on spaces of continuos functions. Along the way we reprove, with these same techniques, a recently found characterization of the dual mixed volume.