410 Index
regularity of a weak solution of
Neumann problem, 128
regularization problem, 14
regularizer, 209
resolvent, 285
restrictions of
Hs(Rn)
to hyperplanes,
53
restrictions of
Hs(Rn)
to ∂Ω, 115
restrictions of distributions to a surface,
63
retarded potential, 76
right regularizer, 210, 211, 274
Robin boundary condition, 108
root vectors, 301, 309
scattering amplitude, 161, 177
scattering matrix, 168
Schr¨ odinger equation, 72, 160
Schwartz’s kernel, 163, 168, 215, 341
second order elliptic operator, 117
second order hyperbolic operator, 342
section of a bundle, 363
selfadjoint operator, 305
semigeodesic coordinates, 290, 295, 300
Shapiro-Lopatinskii condition, 274
sharp arding inequality, 262
signature of a matrix, 335
signature of a quadratic form, 95
simply connected domain, 314
single layer potential, 82, 103, 174
singular integral equation, 327
smoothing operator, 202
Sobolev spaces, 46, 62–67, 128–133
Hs(Ω), 112
Hs(Rn),
46
Hs(∂Ω), 116
Hs
p(Rn),
67
Hp,s(Rn+1),
232
Hp,s(R++1), n
232
W 1,p(Rn), 138
Π
s
m
,s,τ
(R++1), n
223
Π
s
m
,s(Rn+1),
223

Hs(Ω), 112

Hp,s(Rn+1),
232

Π
s
m
,s(Rn+1),
223
duality of, 116
equivalent norm in Hm(Ω), 113
Sobolev’s inequality, 139
stationary phase lemma, 334
strict Huygens principle, 77
strictly hyperbolic operator, 255
strictly hyperbolic polynomial, 232
strongly elliptic operator, 204
symbol of real principal type, 247
symmetric first order hyperbolic
system, 260
tensor product, 319
theorem
Arzel` a-Ascoli, 149
Bott, 320
Cauchy, 224
Egorov’s, 338
Hahn-Banach, 36
Karamata’s Tauberian, 306
Lebesgue convergence, 5
Lidskii’s, 304, 311
Liouville’s, 41, 280, 314
Paley-Wiener, 174
Plancherel’s, 47
Pleijel, 326
Riesz, 36
Sobolev’s embedding, 52
topological index (t-ind), 320
trace class operator, 303
trace of an operator, 304
traces, 53
transition matrices, 264
transport equation, 346
triples (E, F, A(x, ξ)), 318
equivalence classes of, 318
equivalent, 318
isomorphic, 318
triples(E, F, A(x, ξ))
sum of, 318
variational inequality, 135, 137
vector bundle, 264, 278, 319
voltage, 171
wave front set, 217, 348
of a FIO, 340
of solutions of the Cauchy problem,
255
weak solution of the Neumann problem,
127
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