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On a Property of the Legendre Transform. / Mogul’skiĭ, A. A.

в: Siberian Advances in Mathematics, Том 28, № 1, 01.01.2018, стр. 65-73.

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Harvard

Mogul’skiĭ, AA 2018, 'On a Property of the Legendre Transform', Siberian Advances in Mathematics, Том. 28, № 1, стр. 65-73. https://doi.org/10.3103/S1055134418010066

APA

Mogul’skiĭ, A. A. (2018). On a Property of the Legendre Transform. Siberian Advances in Mathematics, 28(1), 65-73. https://doi.org/10.3103/S1055134418010066

Vancouver

Mogul’skiĭ AA. On a Property of the Legendre Transform. Siberian Advances in Mathematics. 2018 янв. 1;28(1):65-73. doi: 10.3103/S1055134418010066

Author

Mogul’skiĭ, A. A. / On a Property of the Legendre Transform. в: Siberian Advances in Mathematics. 2018 ; Том 28, № 1. стр. 65-73.

BibTeX

@article{81073e8f0a5e47efb95fcb05256eb86f,
title = "On a Property of the Legendre Transform",
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).",
keywords = "deviation rate function, generalized inverse function, Legendre transform, logarithm of the Laplace transform",
author = "Mogul{\textquoteright}skiĭ, {A. A.}",
note = "Publisher Copyright: {\textcopyright} 2018, Allerton Press, Inc.",
year = "2018",
month = jan,
day = "1",
doi = "10.3103/S1055134418010066",
language = "English",
volume = "28",
pages = "65--73",
journal = "Siberian Advances in Mathematics",
issn = "1055-1344",
publisher = "PLEIADES PUBLISHING INC",
number = "1",

}

RIS

TY - JOUR

T1 - On a Property of the Legendre Transform

AU - Mogul’skiĭ, A. A.

N1 - Publisher Copyright: © 2018, Allerton Press, Inc.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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).

AB - 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).

KW - deviation rate function

KW - generalized inverse function

KW - Legendre transform

KW - logarithm of the Laplace transform

UR - http://www.scopus.com/inward/record.url?scp=85043499222&partnerID=8YFLogxK

U2 - 10.3103/S1055134418010066

DO - 10.3103/S1055134418010066

M3 - Article

AN - SCOPUS:85043499222

VL - 28

SP - 65

EP - 73

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 1

ER -

ID: 10415538