arXiv Open Access 2007

Generalized Intersection Bodies are not Equivalent

Emanuel Milman

Lihat Sumber

Abstrak

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.

Topik & Kata Kunci

math.FA

Penulis (1)

Emanuel Milman

Format Sitasi

APA MLA BibTeX

Milman, E. (2007). Generalized Intersection Bodies are not Equivalent. https://arxiv.org/abs/math/0701779

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2007
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓