On the approximation of functions on a Hodge manifold

Alessandro Ghigi[1]

  • [1] Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano Bicocca

Annales de la faculté des sciences de Toulouse Mathématiques (2012)

  • Volume: 21, Issue: 4, page 769-781
  • ISSN: 0240-2963

Abstract

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If ( M , ω ) is a Hodge manifold and f ∈ C ∞ ( M , ℝ ) 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.

How to cite

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Ghigi, Alessandro. "On the approximation of functions on a Hodge manifold." Annales de la faculté des sciences de Toulouse Mathématiques 21.4 (2012): 769-781. <http://eudml.org/doc/251007>.

@article{Ghigi2012,
abstract = {If $(M, \omega )$ is a Hodge manifold and $f\in C^\infty (M,\mathbb\{R\})$ we construct a canonical sequence of functions $f_N$ such that $f_N \rightarrow f$ in the $C^\infty $ 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.},
affiliation = {Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano Bicocca},
author = {Ghigi, Alessandro},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Kähler manifold; Hodge manifold; Bergman metric},
language = {eng},
month = {10},
number = {4},
pages = {769-781},
publisher = {Université Paul Sabatier, Toulouse},
title = {On the approximation of functions on a Hodge manifold},
url = {http://eudml.org/doc/251007},
volume = {21},
year = {2012},
}

TY - JOUR
AU - Ghigi, Alessandro
TI - On the approximation of functions on a Hodge manifold
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2012/10//
PB - Université Paul Sabatier, Toulouse
VL - 21
IS - 4
SP - 769
EP - 781
AB - If $(M, \omega )$ is a Hodge manifold and $f\in C^\infty (M,\mathbb{R})$ we construct a canonical sequence of functions $f_N$ such that $f_N \rightarrow f$ in the $C^\infty $ 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.
LA - eng
KW - Kähler manifold; Hodge manifold; Bergman metric
UR - http://eudml.org/doc/251007
ER -

References

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