A Brief Introduction to Berezin-Toeplitz Operators on Compact Kähler Manifolds

This text provides a comprehensive introduction to Berezin-Toeplitz operators on compact Kähler manifolds. The heart of the book is devoted to a proof of the main properties of these operators which have been playing a significant role in various areas of mathematics such as complex geometry, topolo...

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Bibliographic Details
Main Author: Le Floch, Yohann (Author)
Format: Electronic eBook
Language:English
Published: Cham : Springer International Publishing, 2018.
Edition:1st ed. 2018.
Series:CRM Short Courses,
Subjects:
Differential geometry.
Functions of complex variables.
ISBN:9783319946825
ISSN:2522-5200
Online Access: Get full text
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Table of Contents:
  • Preface
  • 1. Introduction
  • 2. A short introduction to Kähler manifolds
  • 3. Complex line bundles with connections
  • 4. Quantization of compact Kähler manifolds
  • 5. Berezin-Toeplitz operators
  • 6. Schwartz kernels
  • 7. Asymptotics of the projector Pi_k
  • 8. Proof of product and commutator estimates
  • 9. Coherent states and norm correspondence
  • A. The circle bundle point of view
  • Bibliography.

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