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＜電子ブック＞
A Brief Introduction to Berezin–Toeplitz Operators on Compact Kähler Manifolds / by Yohann Le Floch
(CRM Short Courses. ISSN:25225219)

版	1st ed. 2018.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2018
大きさ	VIII, 140 p. 161 illus., 1 illus. in color : online resource
著者標目	*Le Floch, Yohann author SpringerLink (Online service)
件　名	LCSH:Geometry, Differential LCSH:Functions of complex variables FREE:Differential Geometry FREE:Several Complex Variables and Analytic Spaces
一般注記	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 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, topological quantum field theory, integrable systems, and the study of links between symplectic topology and quantum mechanics. The book is carefully designed to supply graduate students with a unique accessibility to the subject. The first part contains a review of relevant material from complex geometry. Examples are presented with explicit detail and computation; prerequisites have been kept to a minimum. Readers are encouraged to enhance their understanding of the material by working through the many straightforward exercises HTTP:URL=https://doi.org/10.1007/978-3-319-94682-5

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