[Inversibilité des correspondances de Galois fonctionnelles]
On considère des équations de la forme Bf=g, où B est une correspondance de Galois entre des treillis de fonctions, ce qui inclut le cas où B est la transformation de Fenchel, ou plus généralement une conjugaison de Moreau. Nous caractérisons l'existence et l'unicité d'une solution f, en termes de sous-différentiels généralisés, et étendons ainsi le théorème de couverture de K. Zimmermann pour les équations linéaires max-plus.
We consider equations of the form Bf=g, where B is a Galois connection between lattices of functions. This includes the case where B is the Fenchel transform, or more generally a Moreau conjugacy. We characterize the existence and uniqueness of a solution f in terms of generalized subdifferentials, which extends K. Zimmermann's covering theorem for max-plus linear equations.
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@article{CRMATH_2002__335_11_883_0,
author = {Akian, Marianne and Gaubert, St\'ephane and Kolokoltsov, Vassili},
title = {Invertibility of functional {Galois} connections},
journal = {Comptes Rendus. Math\'ematique},
pages = {883--888},
publisher = {Elsevier},
volume = {335},
number = {11},
year = {2002},
doi = {10.1016/S1631-073X(02)02594-3},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02594-3/}
}
TY - JOUR AU - Akian, Marianne AU - Gaubert, Stéphane AU - Kolokoltsov, Vassili TI - Invertibility of functional Galois connections JO - Comptes Rendus. Mathématique PY - 2002 SP - 883 EP - 888 VL - 335 IS - 11 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02594-3/ DO - 10.1016/S1631-073X(02)02594-3 LA - en ID - CRMATH_2002__335_11_883_0 ER -
%0 Journal Article %A Akian, Marianne %A Gaubert, Stéphane %A Kolokoltsov, Vassili %T Invertibility of functional Galois connections %J Comptes Rendus. Mathématique %D 2002 %P 883-888 %V 335 %N 11 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02594-3/ %R 10.1016/S1631-073X(02)02594-3 %G en %F CRMATH_2002__335_11_883_0
Akian, Marianne; Gaubert, Stéphane; Kolokoltsov, Vassili. Invertibility of functional Galois connections. Comptes Rendus. Mathématique, Tome 335 (2002) no. 11, pp. 883-888. doi : 10.1016/S1631-073X(02)02594-3. http://www.numdam.org/articles/10.1016/S1631-073X(02)02594-3/
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