Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4592164 | Journal of Functional Analysis | 2008 | 19 Pages |
Abstract
We show that an involution T on some class of functions on Rn, which reverses order (meaning that if f⩽g then Tf⩾Tg) has, often, a very specific form, actually essentially unique. It is done in this paper for the class of s-concave functions, for which this unique formula is derived. These functions are, for integer s, exactly marginals of convex bodies of dimension n+s. This understanding is also extended and discussed for other classes of functions, and represents from our point of view the abstract description of the concept of duality.
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