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On the approximation of functions on a Hodge manifold
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 21 (2012) no. 4, pp. 769-781.

Soit (M,ω) une variété de Hodge et soit fC (M,). Nous definissons une suite canonique de fonctions f N telle que f N f dans la topologie C . Cette construction admet une interprétation très simple du point de vue de l’application moment. En plus les fonctions f N sont algébriques réelles, c’est-à-dire qu’elles sont des fonctions régulières sur M vue comme variété algébrique réelle. La définition des f N est inspirée de la quantification de Berezin-Toeplitz et s’appuie sur des idées de Donaldson. La preuve découle très vite de certains résultats dus à Fine, Liu et Ma.

If (M,ω) is a Hodge manifold and fC (M,) we construct a canonical sequence of functions f N such that f N f in the C topology. These functions have a simple geometric interpretation in terms of the moment map and they are real algebraic, in the sense that they are regular functions when M is regarded as a real algebraic variety. The definition of f N is inspired by Berezin-Toeplitz quantization and by ideas of Donaldson. The proof follows quickly from known results of Fine, Liu and Ma.

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DOI : https://doi.org/10.5802/afst.1350
@article{AFST_2012_6_21_4_769_0,
     author = {Alessandro Ghigi},
     title = {On the approximation of functions on a {Hodge} manifold},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {769--781},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 21},
     number = {4},
     year = {2012},
     doi = {10.5802/afst.1350},
     zbl = {1254.32036},
     mrnumber = {3052030},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1350/}
}
Alessandro Ghigi. On the approximation of functions on a Hodge manifold. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 21 (2012) no. 4, pp. 769-781. doi : 10.5802/afst.1350. https://afst.centre-mersenne.org/articles/10.5802/afst.1350/

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