[Caractérisation de l’espace des moments correspondant à la base de Levermore]
Une caractérisation complète de l’espace des moments correspondant à la base de Levermore est donnée ici, à travers des contraintes sur les moments. Les conditions nécessaires sont obtenues grâce à des outils classiques, similaires aux déterminants de Hankel. Dans le cas mono-varié, il est bien connu que ces conditions sont suffisantes. Pour généraliser ce résultat à un cas multi-varié, une preuve constructive non classique est donnée ici en se ramenant à des problèmes mono-variés. Cependant, il est également montré ici, sur un exemple, que la fermeture obtenue dans le cas multi-varié n’hérite pas nécessairement des bonnes propriétés de la fermeture mono-variée.
A complete characterisation of the moment space corresponding to the Levermore basis is given here, through constraints on the moments. The necessary conditions are obtained thanks to classical tools, similar to Hankel determinants. In the mono-variate case, it is well-known that these conditions are sufficient. To generalize this result to multi-variate case, a non-classical constructive proof is given here reducing the problem to several mono-variate ones. However, it is also shown here on an example that the obtained multi-variate closure does not necessarily inherit of the good properties of the mono-variate closure.
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@article{CRMATH_2020__358_1_97_0,
author = {Laurent, Fr\'ed\'erique},
title = {Characterization of the moment space corresponding to the {Levermore} basis},
journal = {Comptes Rendus. Math\'ematique},
pages = {97--102},
publisher = {Acad\'emie des sciences, Paris},
volume = {358},
number = {1},
year = {2020},
doi = {10.5802/crmath.16},
language = {en},
url = {http://www.numdam.org/articles/10.5802/crmath.16/}
}
TY - JOUR AU - Laurent, Frédérique TI - Characterization of the moment space corresponding to the Levermore basis JO - Comptes Rendus. Mathématique PY - 2020 SP - 97 EP - 102 VL - 358 IS - 1 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.16/ DO - 10.5802/crmath.16 LA - en ID - CRMATH_2020__358_1_97_0 ER -
%0 Journal Article %A Laurent, Frédérique %T Characterization of the moment space corresponding to the Levermore basis %J Comptes Rendus. Mathématique %D 2020 %P 97-102 %V 358 %N 1 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.16/ %R 10.5802/crmath.16 %G en %F CRMATH_2020__358_1_97_0
Laurent, Frédérique. Characterization of the moment space corresponding to the Levermore basis. Comptes Rendus. Mathématique, Tome 358 (2020) no. 1, pp. 97-102. doi : 10.5802/crmath.16. http://www.numdam.org/articles/10.5802/crmath.16/
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