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Berezin-Toeplitz quantization on Kaehler manifolds

By Xiaonan Ma and George Marinescu

Abstract

45 pages, footnote at page 3 and Remark 0.5 added; v.3 is a final update to agree with the published paperWe 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

Topics: [ MATH.MATH-DG ] Mathematics [math]/Differential Geometry [math.DG], [ MATH.MATH-CV ] Mathematics [math]/Complex Variables [math.CV], [ MATH.MATH-QA ] Mathematics [math]/Quantum Algebra [math.QA], [ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph], [ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]
Publisher: HAL CCSD
Year: 2012
OAI identifier: oai:HAL:hal-00872364v1
Provided by: Hal-Diderot
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