We prove that in a globally subanalytic family of convex bodies the subfamily of zonoids is log-analytic, and in particular it is definable in the o–minimal structure generated by globally subanalytic sets and the graph of the exponential function. This result establishes a connection between Model theory and Functional analysis.

On tameness of zonoids / Lerario, Antonio; Mathis, Léo. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 282:4(2022). [10.1016/j.jfa.2021.109341]

On tameness of zonoids

Lerario, Antonio;Mathis, Léo
2022

Abstract

We prove that in a globally subanalytic family of convex bodies the subfamily of zonoids is log-analytic, and in particular it is definable in the o–minimal structure generated by globally subanalytic sets and the graph of the exponential function. This result establishes a connection between Model theory and Functional analysis.
282
4
109341
https://arxiv.org/abs/2011.10598
Lerario, Antonio; Mathis, Léo
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/126819
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