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
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