Mathematics – Functional Analysis
Scientific paper
2007-01-26
Mathematics
Functional Analysis
18 pages, added a section with equivalent formulations using Fourier Transforms and Embeddings into L_p for p<0
Scientific paper
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.
No associations
LandOfFree
Generalized Intersection Bodies are not Equivalent does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Generalized Intersection Bodies are not Equivalent, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized Intersection Bodies are not Equivalent will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-568490