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Rudin W. — Functional analysis
Rudin W. — Functional analysis

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Название: Functional analysis

Автор: Rudin W.

Аннотация:

This classic text is written for graduate courses in functional analysis. This text is used in modern investigations in analysis and applied mathematics. This new edition includes up-to-date presentations of topics as well as more examples and exercises. New topics include Kakutani's fixed point theorem, Lamonosov's invariant subspace theorem, and an ergodic theorem.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1973

Количество страниц: 397

Добавлена в каталог: 05.10.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $H^s$      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 $c$, $c_{0}$      83 109
Dual space, of $C(\Omega)$      84
Dual space, of $l^p$      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 $L^2$-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 $L^2$      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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