A Solution to a Question of A. Koldobsky
نویسنده
چکیده
In [Kol00], 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 in [Mil06b], 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 negative answer implies the existence of a non-trivial non-negative function in the range of the spherical Radon transform.
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تاریخ انتشار 2007