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

  • S. Artstein-Avidan (a1), B. Klartag (a2) and V. Milman (a3)


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



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[Mi2]Milman, V. D.. Duality of some geometric characteristics of Banach spaces. Tear. Funksii. Funksional Analiz i Prilozhen, 18 (1973), 120137.
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The Santaló point of a function, and a functional form of the Santaló inequality

  • S. Artstein-Avidan (a1), B. Klartag (a2) and V. Milman (a3)


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