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Spherical projections and centrally symmetric sets. (English) Zbl 0887.52001

Consider the cosine transform \(T\) as a bijection on the Montel space of even smooth functions on the unit sphere in \(n\)-dimensional euclidean space \(\mathbb{R}^n\). Given a convex centrally symmetric body \(K\) in \(\mathbb{R}^n\), denote its support function \(h(K,\cdot)\) and call \(T^{-1}h(K,\cdot)\) the generating distribution of \(K\).
The authors study the main problems that are related to generating distributions. They describe the distributions that generate and study their interrelations with projections.

MSC:

52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
44A12 Radon transform
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References:

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