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

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.

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.

DOI: 10.5802/afst.1350
Alessandro Ghigi 1

1 Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano Bicocca
     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, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 21},
     number = {4},
     year = {2012},
     doi = {10.5802/afst.1350},
     mrnumber = {3052030},
     zbl = {1254.32036},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1350/}
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PB  - Université Paul Sabatier, Institut de Mathématiques
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Alessandro Ghigi. On the approximation of functions on a Hodge manifold. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 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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