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1 results

$\text{SL}(n)$ Invariant Valuations on Super-Coercive Convex Functions
Part of
Fabian Mussnig
Journal:

Canadian Journal of Mathematics / Volume 73 / Issue 1 / February 2021

Published online by Cambridge University Press:

25 October 2019, pp. 108-130

Print publication:

February 2021
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All non-negative, continuous, $\text{SL}(n)$, and translation invariant valuations on the space of super-coercive, convex functions on $\mathbb{R}^{n}$ are classified. Furthermore, using the invariance of the function space under the Legendre transform, a classification of non-negative, continuous, $\text{SL}(n)$, and dually translation invariant valuations is obtained. In both cases, different functional analogs of the Euler characteristic, volume, and polar volume are characterized.