viii CONTENTS
Chapter 13. The FBI transform 291
§13.1. Motivation 291
§13.2. Complex analysis 293
§13.3. FBI transforms and Bergman kernels 302
§13.4. Quantization and Toeplitz operators 311
§13.5. Applications 321
§13.6. Notes 336
Part 4. SEMICLASSICAL ANALYSIS ON MANIFOLDS
Chapter 14. Manifolds 339
§14.1. Definitions, examples 339
§14.2. Pseudodifferential operators on manifolds 345
§14.3. Schr¨ odinger operators on manifolds 354
§14.4. Notes 362
Chapter 15. Quantum ergodicity 365
§15.1. Classical ergodicity 366
§15.2. A weak Egorov Theorem 368
§15.3. Weyl’s Law generalized 370
§15.4. Quantum ergodic theorems 372
§15.5. Notes 379
Part 5. APPENDICES
Appendix A. Notation 383
§A.1. Basic notation 383
§A.2. Functions, differentiation 385
§A.3. Operators 387
§A.4. Estimates 388
§A.5. Symbol classes 389
Appendix B. Differential forms 391
§B.1. Definitions 391
§B.2. Push-forwards and pull-backs 394
§B.3. Poincar´ e’s Lemma 396
§B.4. Differential forms on manifolds 397
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