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| Rudin W. — Functional analysis |
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| Предметный указатель |
*-algebra 305
*-isomorphism 277
Absorbing set 24
Adjoint 92 298 330
Alaoglu, L. 66 375
Alexander, J.W. 383
Algebra 98 115 227
Algebra, commutative 228
Algebra, self-adjoint 115
Algebra, semisimple 268
Almost periodic function 327 377
Annihilator 90 115
Antisymmetric set 115
Approximate identity 157
Arens — Royden theorem 380
Arens, Richard F. 380
Aronszajn, Nachman 381
Ascoli's theorem 369
B*-algebra 276
Baire's theorem 42
Balanced local base 12
Balanced set 6
Ball 4
Banach algebra 228
Banach limit 82
Banach space 4
Banach — Alaoglu theorem 66
Banach — Alaoglu theorem, converse of 108
Banach — Steinhaus theorem 43 44
Banach, Stefan 372 374
Barrel 375
Base of a topology 7
Basis of a vector space 15
Bernstein, Allen R. 381
Beurling, Arne 379
Bilinear mapping 51 54 375
Birkhoff, George D. 374
Bishop's theorem 115 117
Bishop, Errett 377
Blaschke product 118
Bochner's theorem 285 290
Bochner, Salomon 373 381
Bohnenblust, H.F. 375 381
Bonsall, Frank F. 374
Bootstrap proposition 202 378
Borel measure 74
Borel measure, regular 76
Borel set 74
Bounded linear functional 14 23
Bounded linear transformation 23
Bounded set 8 22
Bourgin, Richard D. 376
Branges, Louis de 377
Bray, Hubert E. 374
Browder, Andrew 380
Brown, Aden 376 382
Buck, R. Creighton 374
Calderon, Alberto P. 380
Carleson, Lennart 377
Cartesian product 49
Category 41
Category theorem 42
Cauchy formula 79 205
Cauchy sequence 20
Cauchy — Riemann equation 204
Cauchy's theorem 79
Cayley transform 338
Cech, Eduard 383
centralizer 280
Chain rule 260
Change of measure 347
CHARACTER 166
Characteristic polynomial 198
Choquet's theorem 376
Chover, Joshua 379
Civin, Paul 381 382
Clarkson, James A. 382
Closed convex hull 70
Closed graph theorem 50
Closed operator 329
Closed range theorem 96
Closed set 6
Closure 6
Codimension 38
Cohen, Paul J. 380
Commutator 250 332 382
Compact operator 97
Compact set 7
Complete metric 20
Completely continuous operator 376
Complex algebra 227
Complex homomorphism 231
Complex vector space 5
Complex-linear functional 56
Component 238
Component, principal 257
Cone 319
Conjugate-linear function 292
Continuity 7
Continuity, of scalar multiplication 40
Continuous spectrum 325
Continuously differentiable mapping 249
contour 241
Convergent sequence 7
Convergent sequence, of distributions 146
Convex base 12
Convex combination 36
Convex hull 36
Convex set 6
Convolution 155 166
Convolution algebra 222 230 261 272
Convolution, of distributions 155 159 160 178
Convolution, of measures 219
Convolution, of rapidly decreasing functions 172
de la Vallee-Poussin, Ch.-J. 379
Deckard, Don 381
Deficiency index 341
Degree of polynomial 193
Dense set 14
Densely defined operator 330
Derivation 382
Diagonal 49
Dieudonne, Jean 373
Diffeomorphism 255
Diffeomorphism, local 253
Difference quotient 164 249
Differential operator 33 185 198
Differential operator, elliptic 198
Differential operator, order of 33 198
Differentiation, in Banach algebras 248
Differentiation, of distributions 143
DIMENSION 6 341
Dirac measure 141 150 177
Direct sum 100
Direct sum, of Hilbert spaces 322
Disc algebra 117 230
Distance 4
distribution 136 141
Distribution derivative 143
Distribution, locally  200
Distribution, on a circle 164
Distribution, on a torus 190
Distribution, periodic 190 206
Distribution, tempered 174
Domain 330
Dual space 55
Dual space, of  ,  83 109
Dual space, of  84
Dual space, of  82
Dual space, of a Hilbert space 294 323
| Dual space, of a quotient space 91
Dual space, of a reflexive space 105
Dual space, of a subspace 91
Dual space, of C(K) 66 76
Dual space, second 90 105
Dunford, Nelson 375
Duren, Peter L. 375
Eberlein — Smulian theorem 376
Edwards, Robert E. 376
Ehrenpreis, Leon 192 378
Eigenfunction 107
Eigenvalue 98 311
Eigenvector 98
Elliptic operator 198
Entire function 180
Equicontinuity 43 369
Equicontinuous group 120
Erdos, Paul 379
Essential range 273 303
Essential supremum 83 303
Essentially bounded function 273 303
Evaluation functional 150
Exact degree 193
Exponential function 246 256 317
Extension of holomorphic function 243
Extension theorem 56 57 59
Extremally disconnected space 274
Extreme point 70 286
Extreme set 70
F-space 8
First category 41
Foguel, Shaul R. 381
Ford, J.W.M. 381
Fourier coefficient 53
Fourier coefficient, of a distribution 191
Fourier transform 167
Fourier transform, of  -functions 172
Fourier transform, of convolutions 167
Fourier transform, of derivatives 167
Fourier transform, of polynomials 178
Fourier transform, of rapidly decreasing functions 168
Fourier transform, of tempered distributions 175
Fourier — Plancherel transform 172
Frechet derivative 248
Frechet space 8
Frechet, Maurice 372
Fredholm alternative 107
Fredholm, Ivar 372
Friedrichs, Kurt O. 378
Fuglede, Bent 300 381
Function see also “Functional” “Operator”
Function, almost periodic 327 377
Function, entire 180
Function, essentially bounded 273 303
Function, exponential 246 256 317
Function, harmonic 163 366
Function, Heaviside 164
Function, holomorphic 32 78
Function, infinitely differentiable 33
Function, locally 185
Function, locally integrable 136
Function, positive-definite 290
Function, rapidly decreasing 168
Function, slowly oscillating 211
Function, strongly holomorphic 78
Function, weakly holomorphic 78
Functional 13 (see also “Dual space”)
Functional calculus 380
Functional, bounded 14 23
Functional, complex-linear 56
Functional, continuous 14 55
Functional, linear 13
Functional, multiplicative 230
Functional, on quotient space 91
Functional, on subspace 91
Functional, positive 283
Functional, real-linear 56
Functional, sesquilinear 292
Fundamental solution 192
Gamelin, Theodore W. 380
Gelfand topology 268
Gelfand transform 268
Gelfand — Mazur theorem 237
Gelfand — Naimark theorem 276 380
Gelfand, Izrail M. 237 373 379 380
Gleason, Andrew M. 233 379
Glickfeld, Barnett W. 380
Glicksberg, Irving 377
Goffman, Casper 374
Graph 49 329
Green's function 378
Grothendieck, Alexandre 376
Group, compact 122
Group, of invertible elements 234 257
Group, of operators 120 127 317
Group, topological 122
Haar measure 123 377
Haar measure, of a torus 193
Hadamard, Jacques 379
Hahn — Banach theorems 55-59
Halmos, Paul R. 376 381 382
Hamel basis 52
Harmonic function 163 366
Hausdorff separation axiom 10 49
Hausdorff space 7
Hausdorff topology 7 61
Hausdorff's maximality theorem 367
Heaviside function 164
Heine — Borel property 9
Heins, Maurice 377
Hellinger — Toeplitz theorem 110
Henry, Bruce 379
Hermitian element 275
Hermitian operator 298
Herz, Carl S. 378
Hilbert space 293
Hilbert space, adjoint 298
Hilbert space, automorphism 299
Hilbert transform 191 366
Hilbert, David 372 376
Hilbert-Schmidt operator 376
Hildebrandt, T.H. 374 375
Hille, Einar 380
Holder's inequality 113
Holomorphic distribution 204
Holomorphic function 32
Holomorphic function, of several variables 180
Holomorphic function, vector-valued 78
Homomorphism 167 230 264
Hormander, Lars 378
Horvath, John M. 374
Hyperplane 81
Ideal 263
Ideal, maximal 263
Ideal, proper 263
Idempotent element 247
Image 13
INDEX 79
Inductive limit 377
Infinitesimal generator 355
Ingham's theorem 215
Ingham, Albert E. 379
Inherited topology 7
Inner product 292
Integral of vector function 47 85 179 236 240
Integration by parts 260
Interior 6
Internal point 81
Invariant measure 123
Invariant metric 18
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