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Matematicheskie Zametki, 2020, Volume 107, Issue 3, Pages 323–340
DOI: https://doi.org/10.4213/mzm11898 (Mi mzm11898) 		 
The Extended Legendre Transform and Related Variational Principles

A. B. Antonevicha, E. U. Leonovab

a Belarusian State University
b HiQo Solutions, Inc., Minsk, Belarus
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DOI: https://doi.org/10.4213/mzm11898
Abstract: Variational principles for functionals on the space $C(X)$ of continuous functions that can be written as a representation of a functional in the form of the Legendre transform of the dual functional are considered. The formula of the Legendre transform determines a functional on wider sets of functions, and this functional is called the extended Legendre transform. Functionals that can be represented in the form of the extended Legendre transform are described. Applications to the problem of finding the spectral radius of functional operators are given.
Keywords: Legendre transform, variational principle, spectral radius.
Received: 18.12.2017
English version:
Mathematical Notes, 2020, Volume 107, Issue 3, Pages 369–382
DOI: https://doi.org/10.1134/S0001434620030013
Bibliographic databases:
Document Type: Article
UDC: 517.986
Language: Russian
Citation: A. B. Antonevich, E. U. Leonova, “The Extended Legendre Transform and Related Variational Principles”, Mat. Zametki, 107:3 (2020), 323–340; Math. Notes, 107:3 (2020), 369–382
Citation in format AMSBIB
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