1. On separably integrable symmetric convex bodies.
- Author
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Yaskin, Vladyslav and Zawalski, Bartłomiej
- Subjects
- *
CONVEX bodies , *ELLIPSOIDS , *FOURIER transforms - Abstract
An infinitely smooth symmetric convex body K ⊂ R d is called k -separably integrable, 1 ≤ k < d , if its k -dimensional isotropic volume function V K , H (t) = H d ({ x ∈ K : dist (x , H ⊥) ≤ t }) can be written as a finite sum of products in which the dependence on H ∈ Gr k (R d) and t ∈ R is separated. In this paper, we will obtain a complete classification of such bodies. Namely, we will prove that if d − k is even, then K is an ellipsoid, and if d − k is odd, then K is a Euclidean ball. This generalizes the recent classification of polynomially integrable convex bodies in the symmetric case. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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