On a Property of the Legendre Transform

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Abstract

For a pair of convex lower semicontinuous functions connected by the Legendre transform, we establish that their derivatives are mutually inverse functions (in the generalized sense).

Original languageEnglish
Pages (from-to)65-73
Number of pages9
JournalSiberian Advances in Mathematics
Volume28
Issue number1
DOIs
Publication statusPublished - 1 Jan 2018

Keywords

  • deviation rate function
  • generalized inverse function
  • Legendre transform
  • logarithm of the Laplace transform

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