On a Property of the Legendre Transform

Standard

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

In: Siberian Advances in Mathematics, Vol. 28, No. 1, 01.01.2018, p. 65-73.

Research output: Contribution to journal › Article › peer-review

Harvard

Mogul’skiĭ, AA 2018, 'On a Property of the Legendre Transform', Siberian Advances in Mathematics, vol. 28, no. 1, pp. 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 Jan 1;28(1):65-73. doi: 10.3103/S1055134418010066

Author

Mogul’skiĭ, A. A. / On a Property of the Legendre Transform. In: Siberian Advances in Mathematics. 2018 ; Vol. 28, No. 1. pp. 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.

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