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Complex calculus of variations

Michel Gondran, Rita Hoblos Saade (2003)

Kybernetika

In this article, we present a detailed study of the complex calculus of variations introduced in [M. Gondran: Calcul des variations complexe et solutions explicites d’équations d’Hamilton–Jacobi complexes. C.R. Acad. Sci., Paris 2001, t. 332, série I]. This calculus is analogous to the conventional calculus of variations, but is applied here to 𝐂 n functions in 𝐂 . It is based on new concepts involving the minimum and convexity of a complex function. Such an approach allows us to propose explicit solutions...

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