Isometries for the Legendre-Fenchel transform
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- by Hédy Attouch and Roger J.-B. Wets PDF
- Trans. Amer. Math. Soc. 296 (1986), 33-60 Request permission
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.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 296 (1986), 33-60
- MSC: Primary 49A50; Secondary 52A40, 58E30, 90C25
- DOI: https://doi.org/10.1090/S0002-9947-1986-0837797-X
- MathSciNet review: 837797