Index 361 definition variable coefficient, 47 images, method of, 30–33 inequality of stationary phase, 106 influence curve, 79–83 integration by parts, justification, 61 inviscid compressible fluid dynamics, xv Keller’s blowup theorem, 249 Klein–Gordon equation, 14, 19, 73, 78, 146, 246–257 Kreiss matrix theorem, xii, 88 lagrangian manifold, 213 Lax parametrix, 177–195 Liouville Liouville number, 312 Liouville’s theorem, 238, 311 Littlewood–Paley decomposition, 109, 115, 222, 254 maximally dispersive, 92, 104, 242–246 Maxwell’s equations, xiv characteristic variety, 67 circular and elliptical polarization, 73 eikonal equation, 154 introduction, 44–46 plane waves, 72 propagation cone, 68 rotation of polarization, 288–289 self phase modulation, 287–288 microlocal analysis, xi, xviii elliptic regularity theorem, xviii, 136–140 propagation of singularities theorem, 177–195 applied to stabilization, 195–205 Moser’s inequality, 224, 325 Hs, 284 nondegenerate phase, 182 nondispersive, 99 nonstationary phase, xii and Fourier integral operators, 180–188 and group velocity, 16–20 and resonance, 293, 324 and the stationary phase inequality, 121–122 observability, xviii operator pseudodifferential, xii, 136, 186 transposed, 134 oscillations creation of, 310 homogeneous, 302, 336–338 oscillatory integrals, 180–188 partial inverse for a single phase, 155 multiphase on quasiperiodic profiles, 307 on trigonometric series, 306 of a matrix, 117 perturbation theory, 239 for semisimple eigenvalues, 117–119, 164 generation of harmonics, 262–263 quasilinear, 239 semilinear, 227–230 small oscillations, 259–262 phase velocities, 74, 145 piecewise smooth definition d = 1, 10 function, wavefront set of, 140 solutions for refraction, 38 solutions in d = 1, 11 plane wave, 17, 142–143 polarization in nonlinear geometric optics, 268 linear, circular, and elliptical, 73 of plane waves, 72 rotation of axis, xviii, 288 polyhomogeneous, 182 prinicipal symbol, 64 profile equations quasilinear, 302–314 semilinear, 265–275, 314–315 projection (a.k.a. averaging) operator E, 267–275 propagation cone, 64–71, 75 propagation of singularities, xviii, 1 d = 1 and characteristics, 10–11 d = 1 and progressing waves, 12–16 using Fourier integral operators, 177–195 pulse, see wave purely dispersive, 99–100 quasiclassical limit of quantum mechanics, xvii, 149–151, 160–161, 278
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