Resumen de Intersection bodies and generalized cosine transforms

Boris Rubin

• 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 ?-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 ?-intersection bodies is established. New integral formulas for different classes of cosine transforms are obtained and examples of ?-intersection bodies are given. We also revisit some known facts in this area and give them new simple proofs