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.
Della Vedova, A. (2015). A note on Berezin-Toeplitz quantization of the Laplace operator. COMPLEX MANIFOLDS, 2(1), 131-139 [10.1515/coma-2015-0010].
A note on Berezin-Toeplitz quantization of the Laplace operator
Della Vedova, A
2015
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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