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

• Main Author: Le Floch, Yohann (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: CRM Short Courses,
• Subjects: Differential geometry.; Functions of complex variables.; Differential Geometry.; Several Complex Variables and Analytic Spaces.

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, topol...

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.