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Conformally Invariant Quantization at Order Three

Authors:	Djounga S E Loubon

Institution:	(1) CNRS, Centre de Physique Théorique, Luminy, Case 907, F13288 Marseille Cedex 9, France

Abstract:	Let (M, g) be a pseudo-Riemannian manifold and $\mathcal{F}_{\lambda } (M)$ the space of densities of degree on M. Denote $\mathcal{D}_{{\lambda ,}\mu }^k (M)$ the space of differential operators from $\mathcal{F}_{\lambda } (M)$ to $\mathcal{F}_\mu (M)$ of order k and S _k with = – the corresponding space of symbols. We construct (the unique) conformally invariant quantization map $Q_{{\lambda ,}\mu }^3 :S_\delta ^3 \to \mathcal{D}_{{\lambda ,}\mu }^3$ . This result generalizes that of Duval and Ovsienko.

Keywords:	clusters Gaussian kernels radial basis function networks width scaling factor
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