Intersection bodies and generalized cosine transforms

• Autores: Boris Rubin
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 218, Nº 3, 2008, págs. 696-727
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.01.011
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• Resumen

  • 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