Intersection bodies and generalized cosine transforms

The paper is focused on intimate connection between geometric properties of intersection bodies in convex geometry and generalized cosine transforms in harmonic analysis. A new concept of λ-intersection body, that unifies some known classes of geometric objects, is introduced. A parallel between tra...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2008-06, Vol.218 (3), p.696-727
Main Author: Rubin, Boris
Format: Article
Language:English
Subjects:
Cosine transforms
Intersection bodies
Spherical Radon transforms
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Summary:The paper is focused on intimate connection between geometric properties of intersection bodies in convex geometry and generalized cosine transforms in harmonic analysis. A new concept of λ-intersection body, that unifies some known classes of geometric objects, is introduced. A parallel between trace theorems in function theory, restriction onto lower-dimensional subspaces of the spherical Radon transforms and the generalized cosine transforms, and sections of λ-intersection bodies is established. New integral formulas for different classes of cosine transforms are obtained and examples of λ-intersection bodies are given. We also revisit some known facts in this area and give them new simple proofs.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2008.01.011