|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Reed M., Simon B. — Methods of Functional Analysis (in 4 volumes). Volume 1: Functional Analysis |
|
|
|
| Предметный указатель |
 spaces 68 348-
 ,  ,  ,  94
 -field 23
-finite 23
-ring 23
 argument 26—27
Absolute value of an operator 196
Absolutely continuous subspace 230
Absorbing 127
Adjoint of unbounded operator 252
Adjoint, Banach space 185
Adjoint, Hilbert space 186
Affine linear map 151
Almost everywhere (a.e., ) 17
Analytic completion 336
Analytic Fredholm theorem 201
Analytic function, vector-valued 189—190
Approximate identity 251 326
Ascoli’s Theorem 30
Atomic model 304
B.L.T.theorem 9
Baire category theorem 80
Baire functions 105
Baire measure 105 110
Baire sets 105 110
Balanced 127
Banach space 67
Banach — Alaoglu theorem 115
Banach — Alaoglu theorem, applications 354- 363
Banach — Steinhaus principle see “Principle of uniform boundedness”
Base for a topological space 91
Bergmann kernel 347
Bessel’s inequality 38
Bicontinuous 92
Bijective 2
Bipolar theorem 168
Bochner integral 119
Bochner-Schwartz theorem 331
Bochner’s theorem 330
Bochner’s tube theorem 337
Bolzano -Weierstrass theorem 98
Bore! function 15
Borelsets 14 105
Boson Fock space 53
Boundary 92
Bounded linear transformation 8
Bounded operator 8
Bounded set 165
Bounded variation 33
Brouwer fixed point theorem 364
Canonical form for compact operators 203
Cantor function 21
Cantor set 20
Cartesian product 1
Cauchy net 125
Cauchy principal value 136
Cauchy sequence 5
Chemoff’s theorem 377
Circled 127
Closable form 373
Closable operator 250 252—253
Closed graph theorem 83
Closed operator 250
Closed quadratic form 277
Closure 92
Closure of an operator 250
Cluster point 96
Commuting (unbounded) operators 271—272
Compact operator 199
Compact operator, applications 204—206 368—372
Compact space 98
Compact support, functions of 111
Completely continuous operator see “Compact operator”
Completion 7 9
Cone 109
Connected 95
Continuity of the functional calculus 286—287
Continuous function 6 92
Continuous functional calculus 222
Contraction mapping theorem 151
Convex cone 109
Convex function 356
Convex function, strictly 389
Convex set 109
Convolution 323 324
Core 256
Countable, first 94
Countable, second 94
Cyclic vector 226
Degenerate tube theorem 338
Dense 6
Direct sum of Banach spaces 78
Direct sum of Hilbert spaces 40
Directed family of semi norms 126
Directed system 95
Dirichlet problem 204- 206
Dirichlet’s principle 362
distribution see “Generalized function” “Tempered
Domain 2
Domain of an unbounded operator 249
Dominated Convergence Theorem 17 24
Dual space 43 72
Dunford functional calculus 245
Dunford — Taylor formula 316
Eigenvalue 188
Eigenvector 188
Equicontinuous 29 28—30
Equivalence relation 2
Equivalent family of seminorms 126
Ergodic 58
Ergodic theorem, Birkhoff 60
Ergodic theorem, von Neumann 57
Essential range 229
Essentially self-adjoint 256
Exaggeration 60 1—400
Extension of an operator 250
f.i.p. 98
Fatou’s Lemma 24
Fermion Fock space 54
Filter 352
First resolvent formula 191
Fock space 53
Form core 277
Form domain 276
Form domain, of operator 277
Fourier coefficients 46
Fourier inversion theorem 320
Fourier transform 318
Frechet space 132
Fredholm alternative 203
Fubini’s Theorem 25—26
Functional calculus 222 225 245 263 286—287
Functions of rapid decrease 133
Gauge see “Minkowski functional”
Generalized convergence see “Norm resol vent sense” “Strong
Generalized function 148
Generalized function, of compact support 334
Geodesic 361
Graph 83 250
Graph limit 293—294
Haar measure 155
Hahn — Banach theorem 75—77 130
Hartree equations 359
Hausdorff space 94
Hausdorff — Young inequality 328
Hellinger — Toeplitz theorem 84
Hermitian see “Symmetric operator”
Hilbert space 39
Hilbert — Schmidt operators 210
Hilbert — Schmidt theorem 203
| Holder’s Inequality 68 84 348
Holomorphy domain 336
Holomorphy envelope 336
Homeomorphism 92
Homology group 364
Implicit function theorem 366
Infinitely divisible 341
Injective 2
Inner product 36
Interior 92
Inverse Fourier transform 318
Inverse function theorem 367
Inverse mapping theorem 83
Isometric isomorphism 71
Isometry 7
Kakutani — Krein theorem 104
Kato’s strong Trotter product formula 379
Kernel 185 198
Lebesgue decomposition theorem 22—23 25
Lebesgue measure 15 13—18
Lebesgue — Stieltjes integral 19—2!
Leray — Schauder — Tychonoff theorem 151 365
liminf(dim) 11 12
limsup(lim) 11 12
Linear transformation 2
Linearly ordered 3
Locally compact 110
Locally convex spaces 125
Lower semicontinuous 355
Lusts of the flesh 249
Mackey topology 163
Mackey — Arens theorem 164 167—169
Mapping 1
Markov — Kakutani theorem 152
Maximum principle 382- 384
Measurable functions 15—16
Measure 23 104—111
Measure class 232
Measure, absolutely continuous 22 24
Measure, continuous 22
Measure, pure point 22
Measure, singular 22 24
Metric space 5
Metric transitivity 59
Minimization of functional 354- 363
Minkowski functional 128
Minkowski’s inequality 68 349
Mixing 239
Monotone convergence theorems for forms 372—377
Monotone convergence theorems for functions 17 24
Monotone convergence theorems for nets 106
Montel space 173
Multiplicity free operators 231
Multiplicity theory 231—234
Neighborhood 91
Neighborhood base 91
Nets 96 351
Neumann series 191
Norm 8
Norm resolvent sense, convergence in 284 284—291
Norm, equivalent 71
Normal operator 246
Normal space 94
Normed linear space 8
Nuciear theorem 141 144
One-parameter unitary group 265
Open function 92
Open mapping theorem 82 132
Open set 91
Operator 2
Operator, of uniform multiplicity 233
Orthocomplemented lattice 309—310
Orthogonal 37
Orthogonal complement 41
Orthonormal 37
Orthonormal basis 44 44—46
Paley — Wiener theorem 333
Parallelogram law 38 63
Parseval’s relation 45 46
Partial isometry 197
Partial ordering 3
Pettis’ theorem 119
Phragmen — Lindelof theorems 382—384 391
Plancherel theorem 327
polar 167
Polar decomposition 197 297—298
Polarization identity 63
Positive linear functional 106 350
Positive operator 195
Positive quadratic form 276
Positive type, distribution of 331
Positive type, function of 329
Positive type, weak 331
Principle of uniform boundedness 81 132
Product topology 94
Projection 187
Projection theorem 42
Projection, orthogonal 187
Projection-valued measure (p.v.m.) 234—235 262—263
Pythagorean Theorem 37
Quadratic form 276
quantum mechanics 302—305
Quotient space 78—79
Radon — Nikodym theorem 25 344
RANGE 2
Rectifiable 361
Reflexive space 74 167 174
Regular space 94
Regularity theorem for tempered distributions 139 144
Relative topology 95
Relatively open 95
Reproducing kernel 347
Resolvent 188 253
Resolvent set 188 253
Riemann — Lebesgue lemma 327
Riemann — Stieltjes integral 33
Riesz lemma 43 41—44
Riesz lemma, applications 344—348
Riesz — Markov theorem 107 111 353—354
Riesz — Schauder theorem 203
Schrodinger representation 274
Schwarz inequality 38
Second dual 74
Second quantization 302 309
Self-adjoint operator, bounded 187
Self-adjoint operator, unbounded 255
Self-adjointness, basic criterion for 256—257
Semibounded quadratic form 276
Seminorm 125
Separable 47 95
Separating hyperplane theorem 130—131
Sesquilinear form 44
Singular subspace 230
Singular value of a compact operator 203—204
Spectral mapping theorem 222
Spectral measures 228
Spectral measures, associated with a vector 225
Spectral projections 234
Spectral radius 192
Spectral radius, formula 192
Spectral representation 227
Spectral theorem, functional calculus form 225 263
Spectral theorem, multiplication operator form 225 263
Spectral theorem, p.v.m.form 235 263—264
Spectrum 188
Spectrum, absolutely continuous 231
Spectrum, continuous 231
Spectrum, continuous singular 231
Spectrum, discrete 236
Spectrum, essentia] 236
|
|
|
| Реклама |
|
|
|
|
|
О проекте