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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