INDEX 429
arding, 6, 73, 92–96, 101, 142, 145,
214–216
Gronwall, 117, 265
Hardy–Littlewood–Sobolev, 236
Minkowski, 239
Schur, 82, 314, 327
interpolation, 236, 241, 244
inverse, 91–92
approximate, 400
Inverse Function Theorem, 49, 400, 420
Jacobi’s identity, 20, 21
kernel
Bergman, 293, 307–309
of Fredholm operator, 416
Schwartz, 59, 65, 81, 82, 175, 209,
210, 238, 263, 370, 399
Laplace–Beltrami operator, 157, 243,
351, 353, 357, 362, 378
Leibnitz rule, 150
Lidskii’s Theorem, 413
Lie derivative, 395
lifting, 18–19, 203
Liouville measure, 366
Littlewood–Paley theory, 158, 159, 161,
163, 167, 214
localization, 39, 153, 155, 188, 195
manifolds, 339–363
definition of, 339
PDE on, 353–362
pseudodifferential operators on,
345–352
Riemannian, 344–345
smooth functions on, 340
Maslov index, 264
matrices
J, 15, 16, 64, 257
notation for, 384
symplectic, 252–253, 262
transition, 340
Mean Ergodic Theorem, 367
meromorphic
family of operators, 110, 419
resolvents, 129, 131
microlocality, 195
microlocally invertible, 195
Morse Lemma, 46, 48–50
nondegeneracy condition, 15, 48, 155,
157, 237, 239, 240, 244, 282
nonnormal operators, 287
norm, 140, 346, 347, 371, 387, 411
normal forms, 273–289
complex symbols, 282–286
real symbols, 275–279
notation, 383–389
basic, 383–384
for estimates, 388
for functions, 385–387
for matrices, 384
for operators, 387
for sets, 384
multiindex, 385
observables, 3, 5, 8, 56, 247, 348, 370
Open Mapping Theorem, 417
order functions, 73
change of, 182, 183
definition, 72
examples, 72
log of, 182
order of vanishing, 148–152
oscillatory integral, 6, 40, 46, 52–54
oscillatory testing, 80
phase shift, 36
Planck’s constant, 1, 5
plurisubharmonic functions, 300–302
Poincar´ e’s Lemma, 230, 255, 396
on manifolds, 398
Poisson bracket, 4, 5, 20, 68, 106, 369,
386
polar decomposition, 252
principal symbol, 74, 213, 277, 279, 281,
282, 361, 371
principal type, 276, 278, 282
projection, 127–129, 131, 134, 368, 371,
373
Bergman, 293, 307
propagation of singularities, 279–281
pseudodifferential operators, 2, 4, 55–96
on manifold, 347
symbol of, 348, 349, 351
pseudolocality, 81, 204
pseudospectrum, 287, 288
push-forward, 246, 394
quadratic forms, 295
quantization
and commutators, 61
composition, 66
Fourier decomposition, 65
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