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Matematicheskie Trudy, 2017, Volume 20, Number 1, Pages 145–157
DOI: https://doi.org/10.17377/mattrudy.2017.20.109 (Mi mt319) 		 
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
Full-text PDF (176 kB) Citations (1)
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DOI: https://doi.org/10.17377/mattrudy.2017.20.109
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.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00220_а
Received: 03.05.2016
English version:
Siberian Advances in Mathematics, 2018, Volume 28, Issue 1, Pages 65–73
DOI: https://doi.org/10.3103/S1055134418010066
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
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
Citation in format AMSBIB
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\by A.~A.~Mogul'ski{\v\i}
\paper On a property of the Legendre transform
\jour Mat. Tr.
\yr 2017
\vol 20
\issue 1
\pages 145--157
\mathnet{http://mi.mathnet.ru/mt319}
\crossref{https://doi.org/10.17377/mattrudy.2017.20.109}
\elib{https://elibrary.ru/item.asp?id=29145407}
\transl
\jour Siberian Adv. Math.
\yr 2018
\vol 28
\issue 1
\pages 65--73
\crossref{https://doi.org/10.3103/S1055134418010066}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85043499222}
Linking options:
  • https://www.mathnet.ru/eng/mt319
  • https://www.mathnet.ru/eng/mt/v20/i1/p145
    • This publication is cited in the following 1 articles:
    1. A. A. Borovkov, A. A. Mogul'skii, E. I. Prokopenko, “Properties of the deviation rate function and the asymptotics for the Laplace thansform of the distribution of a compound renewal process”, Theory Probab. Appl., 64:4 (2020), 499–512  mathnet  crossref  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические труды Siberian Advances in Mathematics
    Statistics & downloads:
    Abstract page:386
    Full-text PDF :113
    References:63
    First page:8
     
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