Abstract
The Legendre transform F* of a function F ∈ C 1(R N,R) is defined by the implicit formula
when ∇F is invertible. It has the remarkable property that
or,
so that F* is such that
.
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© 1989 Springer Science+Business Media New York
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Mawhin, J., Willem, M. (1989). The Fenchel Transform and Duality. In: Critical Point Theory and Hamiltonian Systems. Applied Mathematical Sciences, vol 74. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2061-7_2
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DOI: https://doi.org/10.1007/978-1-4757-2061-7_2
Publisher Name: Springer, New York, NY
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