Index

Abel equation, 67

absence of discrete spectrum, 155

adjoint operator, 208

adjoint to ψdo, 214

Agmon’s estimates, 142

Airy function, 380

algebraic multiplicity of λj, 301

amplitude (or symbol) of FIO, 330

analytical index, 321

asymptotics of NB(λ), 305

backscattering amplitude, 191

Beals-Fefferman

classes of ψdo’s, 261

bicharacteristics, 247

Bott isomorphism, 321

Bott periodicity theorem, 321

boundary regularity, 124

boundary value problem, 270

boundary value problem in R+, n 267

canonical transformation, 333, 345, 350

generating function, 333, 346

Cantor function, 32

Carleman’s estimates, 154

Cauchy problem, 70, 72, 73, 223, 232

Cauchy problem with nonzero initial

data, 226

Cauchy-Riemann operator, 107

Cauchy-Schwartz inequality, 37

caustics, 371, 380

characterization of hypoelliptic

polynomials, 89

classes of homotopies, 317

classes of symbols

Pα,m, 224

Pα,m, + 225

Sα,

198

coboundary condition, 398

coboundary problem, 387

coercivity condition, 274

compact operator, 149, 150, 207, 302

composition of ψdo’s, 199

conductivity equation, 171, 300

conservation of energy, 74

continuous deformation, 313, 316

convex functional, 134

convex set, 134

convolution, 24

24

of f ∈ D and g ∈ E , 26

cotangent bundle T

∗(M),

264

critical point, 337

current flux, 171

delta-like sequence, 13

Dirichlet boundary condition, 78, 82,

175, 304

Dirichlet boundary problem, 108, 117,

296

nonhomogeneous, 121

Dirichlet Laplacian, 288

heat kernel, 288

Dirichlet-to-Neumann operator, 84, 168,

169, 297

distorted plane wave, 160, 161, 164, 175

407