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The Santaló point of a function, and a functional form of the Santaló inequality

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

S. Artstein-Avidan ,
B. Klartag  and
V. Milman
S. Artstein-Avidan
Affiliation:
Department of Mathematics, Princeton University, Princeton NJ 08544–1000, USA, and School of Mathematics, Institute for Advanced Study, 1 Einstein Drive, Princeton NJ, 08450, USA E-mail: artstein@math.princeton.edu and artst@math.ias.edu
B. Klartag
Affiliation:
School of Mathematics, Institute for Advanced Study, 1 Einstein Drive, Princeton NJ, 08450, USA E-mail: klartag@math.ias.edu
V. Milman
Affiliation:
School of Mathematical Science, Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel. E-mail: milman@post.tau.ac.il
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Abstract

Let L(f) denote the Legendre transform of a function f: ℝn → ℝ. A theorem of K. Ball about even functions is generalized, and it is proved that, for any measurable function f ≥ 0, there exists a translation f(x) = f(x−a) such that

MSC classification

Secondary: 52A40: Inequalities and extremum problems
Type
Research Article
Information
Mathematika , Volume 51 , Issue 1-2 , December 2004 , pp. 33 - 48
Copyright
Copyright © University College London 2004

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