A new duality transform

Shiri Artstein-Avidan; Vitali Milman

doi:10.1016/j.crma.2008.09.031

A new duality transform

Shiri Artstein-Avidan, Vitali Milman

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

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).

Original language	English
Pages (from-to)	1143-1148
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	346
Issue number	21/22
DOIs	https://doi.org/10.1016/j.crma.2008.09.031
State	Published - 1 Nov 2008

Keywords

MATHEMATICAL transformations
DUALITY theory (Mathematics)
LEGENDRE'S functions
GEOMETRY
MATHEMATICAL functions
MATHEMATICS

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10.1016/j.crma.2008.09.031

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abstract = "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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AB - 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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KW - LEGENDRE'S functions

KW - GEOMETRY

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A new duality transform

Abstract

Keywords

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