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, Leo. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 282:4(2022). [10.1016/j.jfa.2021.109341]
On tameness of zonoids
Lerario, Antonio;Mathis, Leo
2022-01-01
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.File in questo prodotto:
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