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| Zeidler E. — Applied Functional Analysis: Applications to Mathematical Physics |
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| Предметный указатель |
Generalized plane wave 184
Generalized problem 285 306 310
Generalized solution 258
Generalized triangle inequality 8
Generator 298
Geometric series 79
Golden rule for the rate of convergence 143
Golden rule of numerical analysis 143
Graph 414
Graph closed operators 414
Green function 147 157 164 246 251 387 392
Group property 300
Half-numberly spin 357
Hamiltonian 328 371 418
Hamiltonian of the harmonic oscillator 341
Hamiltonian of the hydrogen atom 420
Harmonic oscillation in quantum mechanics 338
Harmonic oscillations 196 303
Heat equation 182
Heisenberg S-operator 402
Heisenberg uncertainty principle 331 342
Hermitean functions 210 339
Hermitean polynomials 210
Hilbert space 107
Hilbert — Schmidt operator 347
Hilbert — Schmidt theory 232
Hoelder continuous functions 96 97
Homeomorphic 28
Homeomorphism 28
Homogeneity in time 302
Hydrogen atom and the Friedrichs extension 420
I (or id), identical operator, Ix:=x for all x 76
Idea of orthogonality 124
Ideal elements 127
Identical operator 77
Infinite series 76
Infinite-dimensional space 6
Initial-value problem 24
Injective 17
Inner product 105
int S, interior of the set S 31
Integer spin 357
Integrable 434
Integral equations 22 62 240
Integral of a step function 432
Integral operator 18 40 265
Integration by parts 117 119 159
Interior 31
Interior point 31
Inverse Fourier transformation 216 378
Inverse operator 17
Inverse scattering theory 406 409
Irreversible process in nature 300 303
Isometric operators 422
Iterated integration 438
Iteration method 18 68 395 404
k-contractive 19
Kato perturbation theorem 417
KdV equation 407
kinetic energy 321 336
KMS-states 360
Knaster, Kuratowski, and Mazurkiewicz lemma 58
Korteweg — de Vries equation 406
L(X, Y),  , spaces of continuous functions 73 79
Lack of classic solution 127
Lagrange multiplier rule 354
Laguerre functions 222
Language of physicists 221 373
Laplacian 125 277 285
Lax pair 412
Lax — Milgram Theorem 174
Least-squares method 201
Lebesgue integral 434
Lebesgue measure 429
Lebesgue spaces 114
Lebesgue — Stieltjes integral 441
Legendre polynomials 209
Leray — Schauder principle 64
Linear combinations 2
Linear continuous functional 74
Linear hull 31
Linear integral equation 23
Linear Lax — Milgram theorem 175
Linear operator 70
Linear orthogonality principle 172
Linear space 3
Linear subspace 30
Linearly independent 5
Lipman — Schwinger integral equation 404
Lipschitz continuous 27
Luzin's theorem 432
Majorant criterion 436
Malgrange — Ehrenpreis theorem 186
Mapping degree 55
Mass conservation 379
Matrix 71
Maximally skew-symmetric 267
Maximally symmetric 267
Maximum 37
Maxwell — Boltzmann statistics 356
Mean continuity 437
meas S, measure of the set S 431
Measurable functions 432
Measurable set 430
Measure 430
Measurements 328 349
Method of finite elements 145
Microscattering processes 400
Mild (generalized) solution 307 311 320 324
Minimal sequence 176
Minimum 37
Minkowski functional 50
Mixed state 358
Models of quantum field theory 368
Momentum operator 342 345 376
Momentum vector 336
Monotone convergence 437
Monotone operators 173
Multiindex 159
Multiplication operator 269 334
Multiplicity 230
N(A) (or ker A), null space (or kernel) of the operator A, N(A):={x:Ax = 0} 70
Navier — Stokes equations 65
Neighborhood 15
Neumann series 79
Newtonian equation 336
Nonexpansive semigroup 299
Nonlinear Fourier transformation 413
Nonlinear Lax — Milgram theorem 175
Nonlinear mathematical physics 173
Nonlinear orthogonality principle 174
Norm 7
Normal order cone 67
Normed space 7
Nuclear spaces 424
Null space 70
Observables 328 359
One-dimensional wave 323
One-parameter group 299
One-parameter unitary group 301 328
open 15
Open neighborhood 15
Operator 16
operator functions 76 77 257
Operator norm 70
Order cone 66
Ordered Banach space 67
Ordered normed space 67
Ordered sets 441
Ordinary differential equations 24 63
| Orthogonal 105
Orthogonal complement 165 178
Orthogonal decomposition 165
Orthogonal projection 165 270
Orthogonality 124
Orthogonality principle 172 175
Orthonormal system 199
Parallelogram identity 123 178
Parameter integrals 439
Parseval equation 203 222
Partial differential equations of mathematical physics 256
Particle number 352
Particle number operator 366
Particle stream 344 403
Partition function 353
path integral 390
Pauli principle 356 363
Payley — Wiener theorem 186 223
Peano theorem 63
Perpendicular principle 123 165
Phase space 393
Photon 340
Physical interpretation of the Green function 158
Physical states 327
Picard — Lindeloef theorem 24
Planck quantum action 329
Planck's radiation law 340 357
Plane wave 184
Poincare inequality 287
Poincare — Friedrichs inequality 136
Poisson equation 125 258 285
Position operator 342 346 377
Positive bilinear form 120
Potential 182
Potential barrier 403
potential energy 321 336
Potential equation 182
Potential theory 95
Pre-Hilbert space 105
Preimage 17
Principle of indistinguishability 363
Principle of maximal entropy 353
Principle of minimal potential energy 256
Principle of minimal potential errors 142
Principle of stationary action 321
Principle of virtual power 142 147
Principle of virtual work 147
probability 336 352
Probability conservation of quantum processes 303
Probability of measuring the position 343
Product rule 107
Propagation of probability 393
Propagator 387
Pure state 358
Pythagorean Theorem 167
Quadratic variational problems 121
Quantization 336
Quantization of action 393
Quantum field theory 363
Quantum hypothesis 340
quantum mechanics 327 336
Quantum statistics 348
Quantum system 327
R(A) (or im A), range (or image) of the operator A 17
r(A), spectral radius of the linear operator A 94
RANGE 17
Rate of convergence 19 142
Real linear space 4
Real normed space 7
Regularity theory 128
Relatively compact 90
Relatively sequentially compact 33
Rellich's compactness theorem 287
Resolvent 83
Resolvent set 83
Resonance condition 249
Restriction 259
Retraction 55
Reversibility 302
Reversible processes in nature 302
Riesz theorem 167
Ritz equation 140 152
Ritz method 140 151 179
S+T, the sum  7
S-matrix 402
Scalar multiplication 3
Scattering of a particle stream 399
Scattering theory 368
Schauder fixed-point theorem 61
Schauder operator 41
Schmidt orthogonalization method 207
Schroedinger equation 323 336 338 381 395
Schwarz inequality 105
Self-adjoint operator 264 416
Semi-Fredholm 83
Semigroup 298
Separability 191
Separable 84 116
Sequentially compact 33
Sequentially continuous 27
Sharp energy 341
Simple eigenvalue 247
simplex 46
Skew-adjoint operator 264
Skew-symmetric operator 264
Smoothing of functions 186
Smoothing technique 117
Sobolev Embedding Theorems 192
Sobolev space 130 260 277
Solitons 406
span S, linear hull of the set S 31
Spectral family 333
Spectral radius 94
Spectral transformation 410
Spectrum 83 94 238
Spectrum of the hydrogen atom 421
Sperner Lemma 56
Sperner simplex 57
Standard model in statistical physics 351 360
States 327 359
Stationary particle states 337
Stationary Schroedinger equation 337
Statistical operator 350
Statistical potential 353
Statistical states 348
Step function 432
Stieltjes integral 333 440
String 158 315
String energy 320
String equation 321
Strong causality 302
Strongly continuous semigroup 298
Strongly monotone operators 173 259 273
Strongly positive bilinear form 120
Subsolution 69
Superposition 196
Superposition of eigenoscillations 317
Superselection rules 328
Supersolution 69
Surjective 17
Symmetric bilinear form 120
Symmetric operator 230 264 415
Tempered delta distribution 221
Tempered distributions 220
Tensor product 224 226
Tensor product of functions 184
Tensor product of generalized functions 185
Theorem 1.A, the Banach fixed-point theorem 19
Theorem 1.B, the Brouwer fixed-point theorem 53
Theorem 1.C, the Schauder fixed-point theorem 61
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