The Extended Legendre Transform and Related Variational Principles

A. B. Antonevich ; E. U. Leonova

Matematičeskie zametki, Tome 107 (2020) no. 3, pp. 323-340.

Résumé

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.

Détail

Mots-clés : Legendre transform
Keywords: variational principle, spectral radius.

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