Abstract
Continuing our search for dualities in different classes of functions, which usually turn out to have an essentially unique form, depending on the class, we exhibit a natural class of functions for which there are exactly two different types of duality transforms. One is the well known Legendre transform, and the other is new. We study the new transform, give a simple geometric interpretation for it, and present some applications. To cite this article: S. Artstein-Avidan, V. Milman, C. R. Acad. Sci. Paris, Ser. I 346 (2008).
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