Generalized Intersection Bodies are not Equivalent
| dc.creator | Milman, Emanuel | |
| dc.date | 2007-01-26 | |
| dc.date | 2007-02-04 | |
| dc.date.accessioned | 2026-07-07T07:44:22Z | |
| dc.date.available | 2026-07-07T07:44:22Z | |
| dc.description | In 2000, A. Koldobsky asked whether two types of generalizations of the notion of an intersection-body, are in fact equivalent. The structures of these two types of generalized intersection-bodies have been studied by the author in [http://www.arxiv.org/math.MG/0512058], providing substantial positive evidence for a positive answer to this question. The purpose of this note is to construct a counter-example, which provides a surprising negative answer to this question in a strong sense. This implies the existence of non-trivial non-negative functions in the range of the spherical Radon transform, and the existence of non-trivial spaces which embed in L_p for certain negative values of p. | |
| dc.description | 18 pages, added a section with equivalent formulations using Fourier Transforms and Embeddings into L_p for p<0 | |
| dc.identifier | https://arxiv.org/abs/math/0701779 | |
| dc.identifier | http://arxiv.org/abs/math/0701779 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123170 | |
| dc.subject | Functional Analysis | |
| dc.title | Generalized Intersection Bodies are not Equivalent | |
| dc.type | text |