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arXiv · 2512.15402

Polynomial local functionals on convex functions

Jonas Knoerr
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Abstract

We show that every continuous local functional on the space of finite convex functions on $\mathbb{R}^n$ is a valuation. This relation is used to establish a homogeneous decomposition for the class of polynomial local functionals as well as a classification of translation or rigid motion invariant polynomial local functionals. In addition we discuss implications for the compact-open topology on the space of polynomial local functionals.

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Jonas Knoerr. 2025-12-17. Polynomial local functionals on convex functions. https://arxiv.org/abs/2512.15402

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