Index 409
initial-boundary value problem for heat
equation, 287
interior regularity, 123
invariance of
Hs(Rn),
55
inverse boundary value problem, 168
inverse obstacle problem, 179
inverse scattering problem, 162
irreducible polynomial, 173
Jordan block corresponding to λj , 301,
304
Lagrangian manifold, 349
conic, 349
Laplace equation, 78
fundamental solution, 78
Laplace-Beltrami operator, 154, 288,
293, 296, 304
left regularizer, 210, 211, 274
Legendre transform, 373
lemma
Fatou, 123
Jordan, 79, 229, 268, 283, 291
Rellich’s, 173, 175, 177
stationary phase, 95, 334
limiting absorption principle, 157, 160
limiting amplitude principle, 102
line bundle, 363
Liouville’s formula, 315, 347
Lippmann-Schwinger equation, 193
local coordinates, 264
manifold, 264
Maslov bundle, 363
Maslov index, 379
maximum principle, 139
meromorphic operator function, 309
method of descent, 108
method of freezing coefficients, 270
metric tensor, 288, 300
microelliptic symbol, 218
minus-operator, 278, 280
minus-symbol, 280
Neumann boundary condition, 82, 175,
177, 293, 304
Neumann data, 84
Neumann Laplacian, 293
heat trace, 294
Neumann problem, 80, 108, 133
Newtonian potential, 78
nondegenerate phase function, 350
nonelliptic boundary value problem, 382
nonhomogeneous Schr¨ odinger equation,
148
nonselfadjoint operator, 301
nonstationary Schr¨ odinger equation,
148
null-bicharacteristic, 247
oblique derivative boundary condition,
328
oblique derivative problem, 382
obstacle problem, 175
operator of order α, 199
orthonormal basis, 302
orthonormal basis of eigenfunctions, 307
outgoing fundamental solution, 156,
161, 174
outgoing solution, 148, 150, 160
parabolic equation, 223
parabolic equation of higher order, 259
parabolic regularization, 235
parametrix, 205, 282
parametrix of a boundary value
problem, 284
Parseval’s equality, 47, 229, 302
partial hypoellipticity, 28
partial hypoellipticity of elliptic
equations, 130
phase function of FIO, 330
Plancherel’s theorem, 71
plus-operator, 278, 280
plus-symbol, 280
Poincar´ e inequality, 118
Poisson bracket, 203
Poisson summation formula, 30
principal symbol of a ψdo on a
manifold, 265
product of distributions, 61
propagation of singularities, 249
pseudodifferential operator on a
manifold, 265
pseudodifferential operator (ψdo), 198
pseudodifferential operator of real
principal type, 247
pseudolocal property of ψdo’s, 217
radiation conditions, 93, 156, 175
radiation conditions in
Rn,
100
Rankine-Hugoniot condition, 32
reduced wave equation, 81
regular functional, 7
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