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The Santaló point of a function, and a functional form of the Santaló inequality
Author(s) -
Artstein-Avidan S.,
Klartag B.,
Milman V.
Publication year - 2004
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300015497
Subject(s) - mathematics , ball (mathematics) , function (biology) , pure mathematics , point (geometry) , legendre polynomials , combinatorics , mathematical analysis , geometry , evolutionary biology , biology
Let L(f) denote the Legendre transform of a function f : ℝ n → 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 1∫ ℝ ne − f ˜∫ ℝ ne − L ( f ˜ )⩽( 2 π ) n .