Hewitt E., Ross K.A. — Abstract Harmonic Analysis (Vol. 2) :: Электронная библиотека попечительского совета мехмата МГУ

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Hewitt E., Ross K.A. — Abstract Harmonic Analysis (Vol. 2)

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Название: Abstract Harmonic Analysis (Vol. 2)

Авторы: Hewitt E., Ross K.A.

Язык:

Рубрика: Математика/Анализ/Продвинутый анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1970

Количество страниц: 771

Добавлена в каталог: 02.04.2005

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Предметный указатель

Semigroup      4 I
Semigroup, cancellation      258 I
Semigroup, topological      98 I 233
Separate points      151 I
Set of spectral resolution      604
Set of spectral synthesis      488
Set of type       552
Shapiro, H. S.      429
Shortley, G. H.      154
Sidon set      416
Sidon set, existence of infinite      428
Sidon, S.      412 413 445 446
Signum (sgn)      3 I
Silov, G. E.      520
Simple algebra      469 I
Simple semigroup      100—101 I
Singular component      653
Singular measure      180 I 269
Skew-Hermitian matrix      7 I
Skew-symmetric matrix      7 I
Solenoidal groups      85 I 409—410
Solenoidal groups, a-adic      114 I
Solenoidal groups, largest      410 I
Solvable group      142
Special linear group      7 I (see also “ $$\mathfrak{S}\mathfrak{L}(n</a></span> <span class=subjpages><a href=$
Special orthogonal group      7 I (see also “ $\mathfrak{S}\mathfrak{D}(n)$ ”)
Special unitary group      7 I (see also “ $\mathfrak{S}\mathfrak{U}(n)$ ”)
Spectral norm of measure      396
Spectral norm of operator      397
Spectral resolution      604
Spectral set      488
Spectral subspaces      545
Spectral synthesis      488
Spectral synthesis, fails for $\mathfrak{L}_1(G)$       597
Spectral synthesis, fails for $\mathfrak{R}(D_2)$       593
Spectral synthesis, fails for $\mathfrak{R}(G)$       597
Spectral synthesis, fails for Banach $\mathfrak{L}_1$ -modules      600
Spectral theorem      488—491 I
Spectral theorem for Hermitian operators      491 I
Spectral theorem, applied      325 I
Spectrally continuous function      396
Spectrum      476 I
Spectrum for $\mathfrak{L}_{\infty}(G)$       522
Spectrum is compact nonvoid      477 I
Spectrum of an ideal      487
Square root of positive-definite operator      485 I 691
Sreider, Yu. A.      519 574
Standard polynomial      474
Steckin, S. B.      446 447
Steinhaus, H.      412 446
Stinespring, W. F.      208
Stone — Weierstrass theorem      151 I 281—282
Stone, M. H.      60 251 322 326 327 518 519
Stone’s theorem      296
Strictly positive linear functional      461 I
Stromberg, K.      679 727
Strong Ditkin sets      604
Stronger topology      9 I
Strongly continuous representation      335 I
Strongly independent sets      574
Structure space      477—478 I
Structure theorem for LCA groups      90 I 389
Subcharacter      607
Subgroup, commutator      358 I 142
Subgroup, normal      16 I
Subgroup, one-parameter      85 I
Subgroup, open and closed      33 —34 I 62
Subgroup, proper      4 I
Subgroup, pure      447 I
Sublinear operator      631
Subnet      14 I
Sufficiently many      343 I
Sufficiently many characters      345 I
Sufficiently many representations      343 I 23
Sugiura, M.      207
Sum of Hilbert spaces      468 I
Sum of linear spaces      452 I
Sum of operators      468 I 688
Summability theorem      648
Summability theorem for compact groups      664
Summability theorem for compact groups, applied      406
Summability theorem for LCA groups      660
Summand of representations      18
Summers, W. H.      290
Support of a function      361
Support of a measure      124 I
Suskevic kernel      101 I
Suzuki, K.      202
Swan, R.      474
Symmetric difference      2 I
Symmetric group $\mathfrak{S}_n$       8 I
Symmetric matrix      7 I
Symmetric norm on       702
Symmetric set      19 I
Symmetric tensors      148
t      31
T, automorphism group of      433 I
T, character group is Z      366 I
T, continuous automorphisms of      369 I
T, Haar measure on      199 I
Taibleson, M.      679
Takahashi, S.      207
Tamarkin, J. D.      414
Tannaka — Krein duality theorem      157 176 178 188
Tannaka, T.      60 157 207 208
Tatsuuma, N.      208
Tauberian theorems      499 510—512
Tensor product      577 680
Tensor product in $\Sigma$       21
Tensor product of Hilbert spaces      686
Tensor product of representations      20
Tensor product of transformations      581 683
Tensor product, complete      578
Thorin, G. O.      252
Titchmarsh, E. C.      251 252
Toeplitz, O.      289 325
Topological automorphism      426 I 208
Topological field      112 I
Topological group      16 I (always $T_0$

after page 83 I)
Topological group, automorphism group of      426—429 I
Topological group, compactly generated      35 I
Topological group, discrete      24 I
Topological group, free      72 I
Topological group, homomorphism groups of      374 I
Topological group, independence of axioms      25 I
Topological group, monothetic      85 I
Topological group, normal      16 I
Topological group, ordered      24 I
Topological group, quotient      40 I
Topological group, real-character      390 I
Topological group, self-dual      422 I

Topological group, solenoidal      85 I
Topological group, solvable      142
Topological group, unimodular      196 I
Topological linear space      453 I
Topological linear space with only one linear functional      371—373 I
Topological linear space, locally convex      453 I
Topological ring      112 I
Topological semigroup      98 I 233
Topologically isomorphic      41 I
Topology, $\Delta$ -      360 I
Topology, Gel’fand      478 I
Topology, norm      454 I
Topology, P-      361 I
Topology, stronger      9 I
Topology, weak      458 I
Topology, weak- $^\ast$       458 I
Topology, weaker      9 I
Topology, Weil      2291
Torsion element in $\Sigma$       66
Torsion group      439 I
Torsion group, compact characterized      406 I
Torsion-free group      439 I
Torsion-free group, compact characterized      406 I
Torsion-free group, divisible characterized      421 I
Torsion-free rank      444 I
Total variation of a measure      169 I
Totally bounded metric space      13 I
Totally disconnected group, small subgroups of      62 I
Totally disconnected space      111
Trace of a matrix      7 I 691
Trace of an operator      687
Transform, Fourier      359 I 478 78
Transform, Fourier — Stieltjes      359 I 78
Transform, inverse      210 228 351
Transformation      2 I
Transitive permutation      46
Transitive set of mappings      8 I
Translate of a function      184 I
Translation      4 I
Translation of functions, continuity of      285 I 305 346
Transpose of a matrix      7 I
Transposition      45
Triangle inequality      453 I
Trigonometric polynomial      5 211
Turan, P.      446
Two-sided ideal in a semigroup      100 I
Two-sided ideal of an algebra      469 I
Two-sided invariant functional      184 I
Two-sided invariant mean      230 I (see also “Invariant means”)
Two-sided invariant pseudo-metric      68 I
Type       722
Type $\Lambda_p$       420
Umegaki, H.      325
Uniform nearness      20 I
Uniform norm      119 I 230
Uniform structures      21 I
Uniform structures, equivalent      21 I
Uniform structures, examples      28 I
Uniformly continuous mapping      21 I
Unimodular group      196 I
Unimodular group, compact      196 I
Unimodular group, equivalent uniform structures      278 I
Uniqueness of T in duality theorem      4241
Uniqueness theorem for Fourier transforms      78 213 231 232
Uniqueness theorem for Fourier — Stieltjes transforms      78 213
Unit ball      453 I
Unit, approximate      303 I
Unit, relative to I      474—475 I
Unitary group      7 I (see also “ $\mathfrak{U}(2)$ ”)
Unitary group, special      7 I (see also “ $\mathfrak{S}\mathfrak{U}(2)$ ”)
Unitary matrix      7 I
Unitary operator      467 I
Unitary representations, continuity equivalences      346 I
Unitary representations, induced      462
Unitary representations, no finite-dimensional      348 I
Upper semicontinuous function      121 I
Urbanik, K.      471
Variation of a measure      169 I
Varopoulos algebra $\mathfrak{B}(E\times F)$       583
Varopoulos, N. Th.      290 313 575 576 602 603 604
Varopoulos’s theorem      270
Vector space      451—452 I
Vector, cyclic      315 I
Veech, W. A.      552
Verblunsky, S.      413 446
Vilenkin, N. YA.      154
von Neumann norms      703
Waerden, B. L. van der      154
Walker, P. L.      551
Wallman, H.      565
Wang, J.      472 509
Warner, C. R.      509 513
Weak direct product of groups      6 I
Weak direct product of groups, character group of      364—365 I
Weak topology      458 I
Weak- $^{\ast}$ topology      458 I
Weaker topology      9 I
Weakly continuous representation      335 I
Weakly measurable representation      335 I
Wedderburn, J. H. M.      693
Weierstrass’s approximation theorem      151 I 281—282
Weight function      144 I
Weil topology      229 I
Weil, A.      37 60 114 115 244 251 252 289 290 325 366 483
Wendel, J. G.      414
Wendel’s theorem      376
Weyl — Peter theorem      24 81
Weyl, H.      37 60 114 153 154 155 323 366 548
Widder, D. V.      520
Wielandt, H.      512
Wiener sets      513
Wiener — Ditkin sets      513
Wiener — Hopf equation      282 I
Wiener, N.      251 506 510 512 518 519 520 521 547 548 550 574
Wiener’s algebra $\mathfrak{M}_1(R)$       506
Wiener’s algebra $\mathfrak{M}_1(R)$ , spectral synthesis fails      600
Wiener’s Tauberian theorems      510
Wigner, E. P.      154 155
Wik, I.      574 575 576 604
Willcox, A. B.      521
Williamson, J. H.      326 574
Word      8 I
WORM      104
Yano, S.      679
Yoshizawa, H.      251
Yosida, K.      197 207 251 326 327 518
Young, W. H.      252 412
Zelazko, W.      469 471
Zero of semigroup      257 I
Zero set of ideal      487
Zuckerman, H. S.      149 442 446 447 448 449 474
Zygmund, A.      216 218 250 286 366 381 400 413 414 436 441 445 446 448 449 674 679

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