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This article is cited in 1 scientific paper (total in 1 paper)
On a property of the Legendre transform
A. A. Mogul'skiĭab a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
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).
Key words:
deviation rate function, logarithm of the Laplace transform,
Legendre transform, generalized inverse function.
Received: 03.05.2016
Citation:
A. A. Mogul'skiǐ, “On a property of the Legendre transform”, Mat. Tr., 20:1 (2017), 145–157; Siberian Adv. Math., 28:1 (2018), 65–73
Linking options:
https://www.mathnet.ru/eng/mt319 https://www.mathnet.ru/eng/mt/v20/i1/p145
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Statistics & downloads: |
Abstract page: | 350 | Full-text PDF : | 101 | References: | 55 | First page: | 8 |
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