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