$\text{SL}(n)$ Invariant Valuations on Super-Coercive Convex Functions
Canadian journal of mathematics, Tome 73 (2021) no. 1, pp. 108-130
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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.
Mots-clés :
valuation, convex function, super-coercive, Legendre transform, SL(n) invariance, polar volume
Mussnig, Fabian. $\text{SL}(n)$ Invariant Valuations on Super-Coercive Convex Functions. Canadian journal of mathematics, Tome 73 (2021) no. 1, pp. 108-130. doi: 10.4153/S0008414X19000531
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author = {Mussnig, Fabian},
title = {$\text{SL}(n)$ {Invariant} {Valuations} on {Super-Coercive} {Convex} {Functions}},
journal = {Canadian journal of mathematics},
pages = {108--130},
year = {2021},
volume = {73},
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doi = {10.4153/S0008414X19000531},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X19000531/}
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