Berezin–Toeplitz quantization on Kähler manifolds

Xiaonan Ma; George Marinescu

doi:10.1515/crelle.2011.133

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Berezin–Toeplitz quantization on Kähler manifolds

Xiaonan Ma George Marinescu

Year: 2011 Journal: Journal für die reine und angewandte Mathematik (Crelles Journal) Publisher: De Gruyter

DOI: 10.1515/crelle.2011.133

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Abstract

We study the Berezin-Toeplitz quantization on Kaehler manifolds. We explain first how to compute various associated asymptotic expansions, then we compute explicitly the first terms of the expansion of the kernel of the Berezin-Toeplitz operators, and of the composition of two Berezin-Toeplitz operators. As application we estimate the norm of Donaldson's Q-operator.

Keywords:

Toeplitz matrix Quantization (signal processing) Mathematics Pure mathematics Kernel (algebra) Asymptotic expansion Norm (philosophy) Toeplitz operator Algebra over a field Mathematical analysis Algorithm

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Geometry and complex manifolds

Physical Sciences → Mathematics → Geometry and Topology

Geometric Analysis and Curvature Flows

Physical Sciences → Mathematics → Applied Mathematics

Advanced Algebra and Geometry

Physical Sciences → Mathematics → Mathematical Physics

Berezin–Toeplitz quantization on Kähler manifolds

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