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The Extended Legendre Transform and Related Variational Principles

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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.

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Authors and Affiliations

  1. Belarusian State University, Minsk, 220030, Belarus

    A. B. Antonevich

  2. HiQo Solutions, Inc., Minsk, 220035, Belarus

    E. Yu. Leonova

Authors
  1. A. B. Antonevich
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  2. E. Yu. Leonova
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Correspondence to A. B. Antonevich or E. Yu. Leonova.

Additional information

Russian Text © The Author(s), 2020, published in Matematicheskie Zametki, 2020, Vol. 107, No. 3, pp. 323–340.

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Antonevich, A.B., Leonova, E.Y. The Extended Legendre Transform and Related Variational Principles. Math Notes 107, 369–382 (2020). https://doi.org/10.1134/S0001434620030013

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