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 G˚ 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