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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access September 28, 2015

A note on Berezin-Toeplitz quantization of the Laplace operator

Alberto Della Vedova
From the journal Complex Manifolds

Abstract

Given a Hodge manifold, it is introduced a self-adjoint operator on the space of endomorphisms of the global holomorphic sections of the polarization line bundle. Such operator is shown to approximate the Laplace operator on functions when composed with Berezin-Toeplitz quantization map and its adjoint, up to an error which tends to zero when taking higher powers of the polarization line bundle.

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Received: 2015-5-15
Accepted: 2015-9-23
Published Online: 2015-9-28

© 2015 Alberto Della Vedova

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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