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| Авторизация |
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| Debnath L., Mikusinski P. — Introduction to Hilbert Spaces with Applications |
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| Предметный указатель |
Homogeneous Dirichlet problem 298
Homogeneous integral equation 224
Homogeneous Neumann problem 298
Homogeneous Volterra equation 239
Idempotent operator 167
Identity operator 138
Image 23
Implicit function theorem 470
Index of performance 447
Infinite dimensional vector space 10
Inner product 88
Inner product space 88
Input function 269
Integral equations 223
Integral of a step function 39
Integral operator 140
Integral over an interval 62
Interaction picture 378 389
Intrinsic angular momentum 400
Inverse differential operators 263
Inverse Fourier transform 201
Inverse image 23
Inverse operator 155
Invertible operator 155
Isometric operator 159
Iterated kernels 240
Jacobian matrix 414
Jacobi’s identity 404
Jacobi’s operator 255
Jacobi’s polynomials 132 255
Kernel 223
kinetic energy 334 353
Klein — Gordon equation 300
Lagrange identity 260
Lagrange’s equations of motion 336 431
Lagrangian 431
Lagrangian function 335
Laguerre operator 255
Laguerre polynomials 130 255
Laplace equation 298 319 320
Laplace operator 298 319 320
Law of conservation of energy 341
Lax 148
Lax — Milgram Theorem 148
Least — Square approximation 455
Lebesgue 37
Lebesgue dominated convergence theorem 60
Lebesgue integrable functions 43 75
Lebesgue integral 43
Lebesgue integral for complex valued functions 72
Lebesgue measure 68
Legendre equation 254 376
Legendre operator 254
Legendre polynomials 100 102 254 376
Linear combinations 9
Linear dependence 9
Linear functional 27
Linear harmonic oscillator 390 394
Linear independence 9
Linear mapping 23
Linear momentum 334 353
Linear operator 138
Linear transformation 138
Lions 445
Lions — Stampacchia theorem 445
Lipschitz’s condition 228 277
Locally integrable complex valued functions 74
Locally integrable functions 62 76
Lowest state energy 392
Lyapounov’s theorem 463
MacNeille 38
magnetic quantum number 337
Matrix Riccati equation 451
Maxwellian distribution 395
Mean value theorem 415
Measurable functions 70
Measurable sets 68
Measure 68
Measurement 349
Method of successive approximation 225 234
Mikusinski 38
Milgram 148
Minkowski’s inequality 8
Momentum density function 372
Momentum wave function 371
Monotone Convergence Theorem 59
Multiple eigenvalue 178
Multiplication operator 140
Multiplicity 178
Multiplier 140
Navier — Stokes equation 322
Neumann 87
Neumann problem 298
Neumann series 227
Newton’s equation 334
Newton’s second law of motion 334 388
Non-degenerate eigenvalue 178
Non-homogeneous equation 224
Non-homogeneous Volterra equation 240
Non-homogenous wave equation 299
Non-separable Hilbert space 125
Nonlinear Fredholm equation 233
Norm 10 51 90 91
Norm in inner product space 91
Norm of a bounded bilinear functional 143
Norm of a bounded quadratic form 144
Norm of uniform convergence 12
Norm,  51
Norm,  75
Norm,  11
Norm, Euclidean 11
Norm, strictly convex 127
Norm, sup 138
Norm, uniform 12
Normal operator 158
Normed space 11
Null function 52
Null operator 138
Null set 54
Null space 23
Observable operators 350
Observables 345
Observation 349
One dimensional Schrodinger equation 394
One-sided shift operator 159
Open balls 14
Open sets 15
Operator 23 138
Operator, adjoint 149 204
Operator, adjoint of a densely defined 204
Operator, adjoint of a differential 250
Operator, angular momentum 396 400 403
Operator, annihilation 392
Operator, anti-Hermitian 155
Operator, associated Legendre 254
Operator, Bessel 256
Operator, bounded 138
Operator, Chebyshev 254
Operator, closed 208
Operator, closed unbounded 208
Operator, commuting 141
Operator, compact 171
Operator, complementary projection 168
Operator, completely continuous 171 176
Operator, creation 392
Operator, densely defined 204
Operator, differential 139
Operator, elliptic 310
Operator, finite dimensional 173
Operator, formally self-adjoint differential 251
| Operator, Fredholm 151
Operator, Hamiltonian 362
Operator, Hammerstein 418
Operator, Heisenberg 385
Operator, Hermite 256
Operator, hermitian 150
Operator, idempotent 167
Operator, identity 138
Operator, integral 140
Operator, inverse 155
Operator, inverse differential 263
Operator, invertible 155
Operator, isometric 159
Operator, Jacobi 255
Operator, Laguerre 255
Operator, Laplace 298 319 320
Operator, Legendre 254
Operator, linear 138
Operator, linear harmonic oscillator 390 394
Operator, linear momentum 334 353
Operator, multiplication 140
Operator, normal 158
Operator, null 138
Operator, observable 350
Operator, one-sided shift 159
Operator, orbital angular momentum 396
Operator, orthogonality of a projection 169
Operator, positive 161
Operator, positive definite 166
Operator, projection 166
Operator, quantum 353
Operator, Schrodinger 385
Operator, self-adjoint 150 206
Operator, square root of a positive 165
Operator, strictly positive 166
Operator, symmetric 206
Operator, time-evolution 379
Operator, total Hamiltonian 389
Operator, two-sided shift 214
Operator, unbounded 203
Operator, unitary 160
Optimal control problems 447
Optimal error 454
Optimal solution 454
Optimal trajectory 448
Optimization problems 424
Orbital angular momentum operators 396
Orbital quantum number 377
Ordinary differential equations 248 268
Orthogonal complement 117
Orthogonal decomposition 121
Orthogonal projection 120
Orthogonal systems 99
Orthogonal vectors 92
Orthogonality of projection operators 169
Orthonormal basis 124
Orthonormal polynomials 458
Orthonormal sequence 99
Orthonormal systems 99
Outcome of quantum measurement 358
Output function 269
Parallelogram law 91
Parseval relation of Fourier transforms 199 201
Parseval’s formula 108
Partial differential equation 295
Particle momentum 369
Pauli’s spin matrices 398
Periodic boundary condition 249
Periodic Sturm — Liouville system 258
Picard’s existence theorem 228
Plancherel theorem 202
Planck 345
Planck’s constant 345
Planck’s simple harmonic oscillator 394
Point spectrum 177
Pointwise convergence 12
Poisson equation 299 305
Poisson’s bracket 343 386
Polarization identity 128 144
Pontrjagin maximum principle 448
POSITION 353
Positive bilinear functional 143
Positive definite operator 166
Positive operator 161
potential energy 334 353
Pre-Hilbert space 88
Principal quantum numbers 377
Principle of linearized stability 462
Principle of quantization 354
Principle of superposition 306
Probability current density 366
probability density 365
Probability flux 366
Product of two operators 141
Projection onto S 121
Projection operator 166
Proper subspace 5
Pythagorean formula 92 104
Quadratic form 143
Quadratic functional 441
Quantization 354
Quantum number 393
Quantum operators 353
Rademacher function 110
RANGE 23
Real vector space 4
Regular distribution 287
Regular points 177
Regular Sturm — Liouville systems 257
Reisz representation theorem 123
Relative extrema 425
Representer of a functional 124
Resolution of a pulse 271
Resolvent 177 235
Riemann integrable functions 64
Riemann integral 64
Riemann — Lebesgue lemma 195
Riesz 58 123
Robin problem 298
Rodrigues formula 377
Root-mean-square deviation 355 359
Scalars 3
Schrodinger picture 378
Schrodinger’s equation 300 362
Schwartz 283
Schwarz’s inequality 90
Second Frechet Derivative 420
Self-adjoint and formally self-adjoint differential operator 251
Self-adjoint operator 150 206
Separability 125
Separable Hilbert spaces 124
Separable kernel 242
Separable spaces 124
Separated boundary conditions 249
Sequence spaces 6
Series of integrable function 50
Sesquilinear functional 143
Set of measure zero 68
Simple eigenvalue 178
Singular distribution 287
Singular Sturm — Liouville system 257
Smooth function 285
Snell’s law 432
Sobolev 97
Sobolev space 96
Solution, asymptotically stable 461
Solution, bifurcation 466
Solution, classical 295
Solution, distributional 296
Solution, equilibrium 461
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