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Complex Manifolds

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A note on Berezin-Toeplitz quantization of the Laplace operator

Alberto Della Vedova
  • Corresponding author
  • Universit`a degli Studi di Milano-Bicocca. Dipartimento di Matematica e Applicazioni. Via Cozzi, 53 - 20125 Milano, Italy
  • Other articles by this author:
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Published Online: 2015-09-28 | DOI: https://doi.org/10.1515/coma-2015-0010

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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About the article

Received: 2015-05-15

Accepted: 2015-09-23

Published Online: 2015-09-28


Citation Information: Complex Manifolds, Volume 2, Issue 1, ISSN (Online) 2300-7443, DOI: https://doi.org/10.1515/coma-2015-0010.

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© 2015 Alberto Della Vedova. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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