Resumen de 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 ?-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
