Index

adjoint, 58

adjoint action, 174

almost analytic extension, 34, 358, 359

annihilation, creation operators, 120

asymptotic sum, 73

atlas, 340

average

in time, 109, 366

of symbols, 372

Beals’s Theorem, 7, 171–177, 179, 180,

196, 216, 249, 271

Bergman kernel, 293, 307–309

Bergman projection, 307

Bergman projector, 293

Birkhoff’s Ergodic Theorem, 367

Borel’s Theorem, 74, 231, 278, 284

Cartan’s formula, 22, 23, 255, 395, 397

Cauchy–Riemann operator, 34, 289, 294

characteristic

equations, 274

variety, 104

closable operator, 405

closed operator, 405

Coarea Formula, 366

coherent state, 102

commutator, 5, 61, 68, 106, 174

compact operator, 87–90, 129, 186,

403–405, 409, 411, 416

composition formula, 6, 66, 160, 175,

178, 186, 193, 194, 263, 268

conjugation, 141, 277, 282

and symbols, 141

by Fourier transform, 56, 64

by unitary operators, 247, 251, 256,

257, 260, 266, 368

contraction of forms, 20, 393

coordinate patch, 340

cotangent bundle, 341

canonical symplectic form, 342

integral over, 342

cotangent space, 342

Cotlar–Stein Theorem, 86, 90, 401

defect measure, semiclassical, 99–117

definition, 101

examples, 102–104

on torus, 108

properties, 104–106

density of states, 132

diffeomorphism, 14, 18, 22, 24, 48, 192,

194, 197, 199, 203, 207, 340, 383,

386

differential, 392

differential forms, 15, 22, 24, 230, 342,

391–398

canonical, 342

differential operator, 345

distribution, 35, 58, 76, 345, 347, 387,

399

domain of operator, 405

Duhamel’s formula, 154, 234, 270, 271

dynamics

classical, 1, 4, 8, 13–14, 106, 272, 274

operator, 181, 220–227, 246

427