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| Rudin W. — Functional analysis |
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| Предметный указатель |
Invariant subspace 310 382
Invariant topology 8
Inverse 231 346
Inverse function theorem 252
Inverse image 13
Inversion theorem 170
Invertible element 231
Invertible operator 98
Involution 275
Kahane, Jean-Pierre 233 376 379
Kakutani's fixed point theorem 120
Kakutani, Shizuo 374 377 379
Kaplansky, Irving 380 382
Karlin, Samuel 219 379 381
Kleinecke, David C. 382
Kolmogorov, A. 374
Korevaar, Jacob 379
Krein — Milman theorem 70 377
Krein, M. 375 376
Laplace equation 197
Laplacian 189
Lax, Peter D. 378
Le Page, Claude 380
Le Veque, William J. 379
Lebesgue decomposition 219
Lebesgue integral 372
Lebesgue spaces 31 35 111
Left continuity 228
Left multiplication 229
Left shift 259
Left translate 122
Leibniz formula 144 145
Levinson, Norman 379
Lewy, Hans 378
Liapounoff, A. 377
LIMIT 7
Lindenstrauss, Joram 377
Linear functional see “Functional”
Linear mapping 13
Liouville's theorem 81
Lipschitz space 40
Littlewood's tauberian theorem 209 222
Littlewood, John E. 208 378
Local base 7 122
Local base, balanced 12
Local base, convex 12
Local compactness 8
Local convexity 8 24
Local diffeomorphism 253
Local equality of distributions 147
Local finiteness 147
Locally  function 185
Locally bounded space 8
Locally convex space 8
Locally integrable function 136
Logarithm 246
Lorch, Edgar R. 374 380 382
Lumer, Gunter 381
Malgrange, Bernard 192 378
Mandelbrojt, Szolem 374
Mapping see also “Operator”
Mapping, bilinear 51 54 375
Mapping, continuously differentiable 249
Mapping, open 29 46
Max-min duality 376
Maximal ideal space 268
Maximally normal operator 350
Maximally symmetric operator 337
McShane, Edward J. 374
Measure, Borel 74
Measure, H-valued 302
Measure, Haar 123
Measure, nonatomic 113
Measure, normalized Lebesgue 166
Measure, probability 74
Measure, projection-valued 302
Measure, regular 76
Mergelyan's theorem 117
Metric 4
Metric space 4
Metric, compatible 7
Metric, complete 20
Metric, Euclidean 14
Metric, invariant 18
Metrization theorem 18 61 374
Metrization theorem, in locally convex spaces 27 28
Milman, D. 375
Minkowski functional 24
Monomial 142
Montel space 375
Multi-index 32
Multiplication operator 318 325
Multiplication theorem 343
Multiplicative functional 230
Multiplicative inequality 227
Nagumo, M. 373
Naimark, M. A. 380
Neighborhood 7
Neumann, John von 373 374 376 377 382
Ney, Peter 379
Nonatomic measure 113
Norm 4
Norm topology 4
Norm, in dual space 89
Normable space 8
Normal element 281
Normal operator 298 348
Normal subset 281
Normalized Lebesgue measure 166
Normed dual 87
Normed space 4
Nowhere dense set 41
Null space 13
Open mapping 29
Open mapping theorem 46
Open set 6
Operational calculus 380
Operator, bounded 23
Operator, closed 329
Operator, compact 97
Operator, completely continuous 376
Operator, densely defined 330
Operator, differential 33 185 198
Operator, elliptic 198
Operator, hermitian 298
Operator, invertible 98
Operator, linear 13
Operator, maximally normal 350
Operator, maximally symmetric 337
Operator, normal 298 348
Operator, positive 313 349
Operator, self-adjoint 298 331
Operator, symmetric 110 331
Operator, unitary 298
Order, of a differential operator 198
Order, of a distribution 141
Order, of an operator on Sobolev spaces 199
Order, partial 367
Order, total 367
Origin 5
Original topology 63 64
Orthogonal complement 294
Orthogonal vector 292
Paley — Wiener theorems 181 183
Parallelogram law 293
Parseval formula 172
Partial isometry 316
Partially ordered set 367
Partition 85
Partition, of unity 147
| Pearcy, Carl M. 381 382
Pettis, Billy J. 375
Pick — Nevanlinna problem 118
Pitt's theorem 212 220
Pitt, Harry R. 211 379
Plancherel theorem 172
Plancherel, M. 378
Point spectrum 247 312 325
Polar decomposition 315 364
Polar of a set 66
Pole 261
Polydisc 267
Polydisc algebra 288
Polynomial convexity 272
Positive functional 283 319
Positive operator 313 349
Positive-definite function 290
Preimage 13
Prime number theorem 212
Principal component 257
Principal part of operator 198
Principal value integral 165
Probability measure 74
Product topology 49
Projection 126 298 299
Ptak, Vlastimil 381
Putnam, Calvin R. 300 381
Quotient algebra 264
Quotient map 29
Quotient norm 30
Quotient space 29
Quotient topology 29
Radical 268
RANGE 94
Rapidly decreasing function 168
Real vector space 5
Reflexive space 90 104 382
Regularity theorem 197 201
Renewal equation 218
Residual spectrum 325
Resolution of identity 301 341 348
Resolvent set 234 346
Riemann zeta function 214
Riemann — Lebesgue lemma 378
Riemann, Bernhard 373
Riesz representation theorem 53
Riesz, Frederic 117 372 376 382
Riesz, Marcel 117 130
Right continuity 228
Right multiplication 229
Right shift 259
Right translate 122
Riviere, Nestor M. 380
Robinson, Abraham 381
Rogosinski, Werner W. 376
Romberg, Bernard W. 375
Root 246
Rosenblum, Marvin 300 381
Rosenthal, Haskell, P. 377
Royden, Halsey L. 380
Runge's theorem 244
scalar 5
Scalar field 5
Scalar multiplication 5
Schaffer, Juan J. 381
Schauder, J. 376
Schneeberger, Charles M. 382
Schwartz, Laurent 373 378
Schwarz inequality 293
Second category 41
Second dual 90 105
Seid, Howard A. 379
Selberg, Atle 379
Self-adjoint algebra 115
Self-adjoint element 275
Self-adjoint operator 298
Semigroup 355
Semigroup, of normal operators 360
Semigroup, unitary 360
Seminorm 24
Semisimple algebra 268
Separable space 68
Separate continuity 51
Separating family 24
Separation theorems 9 58 70
Sequential continuity 370
Sesquilinear functional 292
Set, absorbing 24
Set, antisymmetric 115
Set, balanced 6
Set, Borel 74
Set, bounded 8 22
Set, closed 6
Set, compact 7
Set, convex 6
Set, dense 14
Set, extreme 70
Set, normal 281
Set, nowhere dense 41
Set, of first category 41
Set, of second category 41
Set, open 6
Set, partially ordered 367
Set, totally ordered 367
Set, weakly bounded 64
Shapiro, Harold S. 376
Shapiro, Joel H. 375
Shields, Allen L. 375 376
Shift operator 106
Shilov boundary 290
Siddiqui, Jamil A. 379
Slowly oscillating function 211
Smith, Kennan T. 381
Smulian, V. 376
Sobczyk, Andrew 375 377
Sobolev spaces 199 378
Sobolev's lemma 185
Sobolev, S.L. 373 378
Soukhomlinoff, G.A. 375
Space, Banach 4
Space, barreled 375
Space, complete metric 20
Space, extremally disconnected 274
Space, Frechet 8
Space, Hilbert 293
Space, Lipschitz 40
Space, locally bounded 8
Space, locally compact 8
Space, locally convex 8
Space, metric 4
Space, Montel 375
Space, normable 8
Space, normed 4
Space, quotient 29
Space, reflexive 90 104 382
Space, separable 68
Space, topological 6
Space, totally disconnected 370
Space, uniformly convex 327 382
Space, unitary 292
Space, vector 5
Space, with Heine — Borel property 9
Spectral decomposition 309 348 351
Spectral mapping theorem 244 247
Spectral radius 234
Spectral radius, formula 235
Spectral theorem 305 348 351
Spectrum 98 234 346
Spectrum, continuous 325
Spectrum, of compact operator 103
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