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Isometries for the Legendre-Fenchel transform

Authors: Hédy Attouch and Roger J.-B. Wets
Journal: Trans. Amer. Math. Soc. 296 (1986), 33-60
MSC: Primary 49A50; Secondary 52A40, 58E30, 90C25
MathSciNet review: 837797
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Abstract: It is shown that on the space of lower semicontinuous convex functions defined on $ {R^n}$, the conjugation map--the Legendre-Fenchel transform--is an isometry with respect to some metrics consistent with the epi-topology. We also obtain isometries for the infinite dimensional case (Hilbert space and reflexive Banach space), but this time they correspond to topologies finer than the Moscoepi-topology.

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Keywords: Convexity, epi-convergence, variational convergence, duality, conjugation, Legendre-Fenchel transform, isometry, polarity
Article copyright: © Copyright 1986 American Mathematical Society

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