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

-set      552
-set      552
      269 I (see also “ $\mathfrak{L}_1(G)$ ”)
, isomorphic with $\mathfrak{L}_1$       272 I
$\alpha$ -mesh      13 I
$\delta$ -topology      360 I
$\Delta_a$       109 I 416—417
$\Delta_a$ , character group of      402 I
$\Delta_a$ , Haar measure on      202 I
$\Delta_p$       109 I
$\Delta_p$ , automorphism group of      434 I
$\Delta_p$ , minimal divisible extension of      419 I
$\iota$ -almost everywhere      124 I
$\iota$ -measurable function      125 I
$\iota$ -measurable set      125 I
$\iota$ -null function      124 I
$\iota$ -null set      124 I
$\Lambda_p$ set      420
$\mathbb{Q}$ (rational numbers)      3 I
$\mathbb{Q}$ , character group of      404 I 414
$\mathbb{R}$ (real line)      3 I
$\mathbb{R}$ is open continuous homomorph of totally disconnected group      50 I
$\mathbb{R}$ , automorphism group of      433 I
$\mathbb{R}$ , character group is R      367 I
$\mathbb{R}$ , compact connected topology for      415 I
$\mathbb{R}$ , continuous homomorphisms of      370 I
$\mathbb{R}$ , Haar measure on      198 I
$\mathbb{R}$ , invariant mean for $\mathfrak{U}_c(R)$       256 I
$\mathbb{R}$ , invariant means for $\mathfrak{B}^r(R)$       240 I
$\mathbb{R}$ , topologies in      27 I
$\mathbb{R}^n$       3 I
$\mathbb{R}^n$ , automorphism group of      434 I
$\mathbb{R}^n$ , characterized      104 I
$\mathbb{R}^n$ , closed subgroups of      92 I
$\mathbb{Z}$ (integers)      3 I
$\mathbb{Z}$ , character group is T      366 I
$\mathbb{Z}$ , invariant mean for $\mathfrak{U}(Z)$       256 I
$\mathbb{Z}$ , nondiscrete topology for      27 I
$\mathfrak{B}\mathfrak{L}(n, F)$       7 I
$\mathfrak{B}\mathfrak{L}(n, F)$ has inequivalent uniform structures      28—29 I
$\mathfrak{B}\mathfrak{L}(n, F)$ is locally Euclidean      29—31 I
$\mathfrak{B}\mathfrak{L}(n, F)$ , Haar measure on      201 I 209
$\mathfrak{B}\mathfrak{L}(n, F)$ , left invariant metric on      78 I
$\mathfrak{D}(3)$ , representations of      151
$\mathfrak{D}(n)$       7 I
$\mathfrak{D}(n)$ is compact      29 I
$\mathfrak{D}(n)$ is locally Euclidean      29—31 I
$\mathfrak{G}^{\ast}_0(X)$ as convolution algebra      265 I
$\mathfrak{G}^{\ast}_0(X)$ , adjoint operation in      299 I
$\mathfrak{G}^{\ast}_0(X)$ , equivalent with M(G)      269 I
$\mathfrak{G}_0(X)$       119 I
$\mathfrak{G}_0(X)$ , characterized as Banach algebra      481 I
$\mathfrak{G}_0(X)$ , closed ideals in      483 I
$\mathfrak{G}_0(X)$ , conjugate space of      170 I 175
$\mathfrak{G}_0(X)$ , multiplicative linear functionals of      484 I
$\mathfrak{G}_0(X)$ , structure space is X      484 I
$\mathfrak{G}_{00}(X)$       119 I
$\mathfrak{G}_{00}(X)$ , nonnegative linear functionals on      120 I
$\mathfrak{G}_{00}(X)$ , unbounded linear functionals on      167 I
$\mathfrak{L}_1(G)$ has approximate unit      303 I
$\mathfrak{L}_1(G)$ has no unit      303 I
$\mathfrak{L}_1(G)$ , all $\sim$ -representations      294
$\mathfrak{L}_1(G)$ , and $\mathfrak{C}_{00}(X)$       573
$\mathfrak{L}_1(G)$ , center of      85 109
$\mathfrak{L}_1(G)$ , commutative if and only if G is      302 I
$\mathfrak{L}_1(G)$ , Ditkin’s condition      501
$\mathfrak{L}_1(G)$ , factorization in      271 515
$\mathfrak{L}_1(G)$ , ideals characterized      303 I
$\mathfrak{L}_1(G)$ , isomorphic with       272 I
$\mathfrak{L}_1(G)$ , spectral synthesis fails      597
$\mathfrak{L}_2(G)$ , invariant subspaces      237
$\mathfrak{L}_p$ conjecture      469 471
$\mathfrak{L}_p$ Fourier transform      225 227
$\mathfrak{L}_p(G)$ -maximal function      606 607
$\mathfrak{R}(G)$       260 330 338
$\mathfrak{R}(G)$ , as convolution algebra      352
$\mathfrak{R}(G)$ , Ditkin’s condition      344
$\mathfrak{R}(G)$ , spectral synthesis fails      597
$\mathfrak{R}(G)$ , structure space      340
$\mathfrak{S}\mathfrak{D}(3)$ , representations of      136—141
$\mathfrak{S}\mathfrak{D}(n)$       71
$\mathfrak{S}\mathfrak{D}(n)$ is compact      29 I
$\mathfrak{S}\mathfrak{D}(n)$ is locally Euclidean      29—31 I
$\mathfrak{S}\mathfrak{L}(n,F)$       7 I
$\mathfrak{S}\mathfrak{L}(n,F)$ has inequivalent uniform structures      28—29 I
$\mathfrak{S}\mathfrak{L}(n,F)$ has no finite-dimensional unitary representations      350 I
$\mathfrak{S}\mathfrak{L}(n,F)$ is locally Euclidean      29—31 I
$\mathfrak{S}\mathfrak{L}(n,F)$ , homomorphisms into $[0,\infty)$       212—213 I
$\mathfrak{S}\mathfrak{U}(2)$ , Haar measure on      134
$\mathfrak{S}\mathfrak{U}(n)$       71
$\mathfrak{S}\mathfrak{U}(n)$ , representations of      125—136
$\mathfrak{S}\mathfrak{U}(n)$ is compact      29 I
$\mathfrak{S}\mathfrak{U}(n)$ is locally Euclidean      29—31 I
$\mathfrak{S}\mathfrak{U}(n)$ , Hewitt and Ross, Abstract harmonic analysis      vol II
$\mathfrak{T}(G)$ (trigonometric polynomials)      5 211
$\mathfrak{T}(G)$ (trigonometric polynomials) is dense in $\mathfrak{C}(G)$       23
$\mathfrak{T}(G)$ (trigonometric polynomials) is dense in $\mathfrak{L}_p(G)$       211
$\mathfrak{T}(G)$ (trigonometric polynomials) is Krein algebra      163
$\mathfrak{T}(G)$ (trigonometric polynomials), invariant subspaces      204 473
$\mathfrak{T}(G)$ (trigonometric polynomials), linear functionals on      157 161 178—187
$\mathfrak{T}(G)$ (trigonometric polynomials), orthogonality relations      8 11 14
$\mathfrak{U}(2)$ , representations of      150
$\mathfrak{U}(G)$       247 I 302
$\mathfrak{U}(G)$ , existence of invariant means      250 I
$\mathfrak{U}(G)$ , uniqueness of invariant means      252 I
$\mathfrak{U}(H)$       115 (see also “ $\mathfrak{U}(n)$ ”)
$\mathfrak{U}(n)$       7 I
$\mathfrak{U}(n)$ is arcwise connected      64 I
$\mathfrak{U}(n)$ is compact      29 I
$\mathfrak{U}(n)$ is locally Euclidean      29—31 I
$\mathfrak{U}(n)$ , closed subgroups      101 194 663
$\mathfrak{U}(n)$ , integrals on      115—124 146
$\omega$ -functions      259 I
$\Omega_a$       108 I
$\Omega_a$ , character group of      400 I
$\Omega_a$ , closed subgroups      116 I
$\Omega_a$ , Haar measure on      202—203 I
$\Omega_r$       109 I
$\Omega_r$ , automorphism group of      433 I
$\Omega_r$ , character group is $\Omega_r$       400 I
$\Sigma$       2 (see also “Dual object”)
$\sigma$ -algebra of sets      118 I
$\sigma$ -bounded set      93
$\sigma$ -compact spaces      111
$\sigma$ -compact spaces, product of      13 —14 I
$\sigma$ -finite set function      118 I
$\sigma$ -locally finite      13 I
$\sigma$ -ring of sets      118 I
$\sigma(E, \mathfrak{F})$ topology      717
$\sim$ -representation      314 I
$\sup P_{\gamma}$       632
$\varepsilon$ -mesh      13 I
0-dimensional group, small subgroups of      62 I
0-dimensional space      11 I
a-adic integers      109 I (see also “ $\Delta_a$ ”)
a-adic numbers      109 I (see also “ $\Omega_a$ ”)
a-adic solenoid      114 I
Abelian group      see “Group”
Abelian group, nondiscrete topologies      27 I
Absolutely continuous measure      180 I 269
Absolutely convergent Fourier series      330
Abstract Tauberian theorem      499
Act disjointedly      719
Additive function      452 I
Adjoint homomorphism      392 I
Adjoint homomorphism, generalized      203
Adjoint in $\mathfrak{B}^{\ast}(G)$       310 I
Adjoint in $\mathfrak{G}^{\ast}_0(G)$       299 I
Adjoint in $\mathfrak{G}^{\ast}_u(G)$       310 I
Adjoint in an algebra      313 I

Adjoint in M(G)      300 I
Adjoint operator      466 I 711 712
Agmon, S.      521
Akemann, C. A.      113 414 447
Alaoglu’s theorem      458 I
Algebra      469 I
Algebra of sets      118 I
Algebra with adjoint operation      313 I
Algebra, $\sim$ -algebra      313 I
Algebra, convolution      263 I
Algebra, homomorphism      470 I
Algebra, imbedded in algebra with unit      470 I
Almost everywhere      124 I
Almost periodic compactification      311
Almost periodic function      247 I (see also “ $\mathfrak{U}(G)$ ”)
Alternating group      46
Ambrose, W.      326
Amitsur, A. S.      474
Analytic functions operating in algebras      490 603
Annihilator of $P \subset \Sigma$       62
Annihilator of $X \subset G$       365 I 64
Annihilator, generalized      202
Anti-symmetric tensors      148
Approximate unit      303 I
Approximate unit for $\mathfrak{L}_1(G)$       303 I 107
Approximate unit for compact groups      88 273 286 335
Approximate unit for LCA groups      298
Approximate unit, bounded      87
Approximation theorems      431—432 I 435
Arbitrarily small sets      62 I
Arcwise connected space      111
Artin, E.      143
Automorphism group      426—429 I
Automorphism group, examples      433 I
Automorphism group, inner automorphism subgroup      439 I
Automorphism group, modular function of      438 I
Automorphism group, non locally compact      435 I
Automorphism, inner      4 I
Automorphism, topological      426 I 208
Babenko, K. I.      630
Baire category theorem      42 I 456
Baire measurable function      118 I
Baire sets      118 I
Baire sets and Haar measure      280 I
Balanced neighborhood      453 I
Banach $\sim$ -algebra      313 I
Banach A -module      263
Banach algebra      469 I
Banach algebra in $\mathfrak{G}(X)$       484
Banach algebra in $\mathfrak{G}_0(X)$ , where X is the structure space      489
Banach fields, characterized      473 I
Banach modules in $\mathfrak{L}_1(X)$       451 502
Banach modules in $\mathfrak{L}_1(X)$ , spectral synthesis fails      600
Banach space      455 I
Banach space, reflexive      457 I
Banach space, weak topology      458 I
Banach space, weak- $^{\ast}$ topology      458 I
Banach — Steinhaus theorem      456 I
Banach, S.      435 446 447
Bari, N. K.      250 366
Basis of a group      442 I
Basis of a linear space      681
Basis of a measure space      215 I
Basis, orthonormal      465 I
Belong locally      495
Bernstein, S.      441
Berry, A. C.      251 327
Beurling, A.      519 521 522 549 550 551 601 605
Bieberbach, L.      445
Bilinear functional      453 I
Bilinear functional, bounded      468 I
Bird      210
Birkhoff, G.      6 45 683
Blocks of Krein algebra      162
Bochner, S.      206 250 251 289 325 326 327 413 448 520 549
Bochner’s theorem      293 160
Boerner, H.      153 155
Bohr compactification      430 I 302
Bohr, H.      312 448 519
Boolean $\sigma$ -homomorphism      316
Borel measurable function      118 I
Borel sets      118 I
Boundary      497
Bounded bilinear functional      468 I
Bounded left approximate unit      87 (see also “Approximate unit”)
Bounded linear function      454 I
Bounded linear function, relatively      461 I
Bounded order      439 I
Bounded order, characterized      449 I
Bourbaki, N.      115
Brainerd, B.      414 434
Bunyakovskii’s inequality      137 I
Burckel, R. B.      310 399 726
Burckhardt, H.      250
Burnside, W.      54 59 60 480
Calderon sets      513
Cancellation laws      98—99 I
Cancellation semigroup      258 I
Caratheodory outer measure      123 I
Caratheodory, C.      325
Cardinal number of character groups      382 I 396
Cardinal number of dual objects      43 61 99
Cardinal number of nondiscrete locally compact groups      31 I
Cardinal number, notation for      2 I
Carleman, T.      251 435 520
Carleson set      575
Carleson, L.      574 575
Cartan, E.      153 548
Cartan, H.      250 251 253 309 310 327
Cartesian product of sets      2 I
Category, Baire      456 I
Category, theorem of Baire      42 I 456
Cauchy — Bunyakovskii — Schwarz inequality      464 I
Cauchy’s inequality      137 I
Cayley, A.      156
Cech, E.      99
Center of $\mathfrak{L}_1(G)$       85 109
Center of a semigroup      84
Center of a topological group      46 I 65 4291
Center of an algebra      84
Central element      84
Central functions      84
Central measures      84
Chandrasekharan, K.      520
Character group      355 I
Character group and structure space of       358—361 I
Character group of       404 I 414
Character group of       405 I
Character group of       405 I
Character group of $\Delta_a$       402 I
Character group of $\Omega_a$       400 I
Character group of $\Sigma_a$       403 I
Character group of closed subgroup      380 I
Character group of finite group      367 I
Character group of local direct product      373 I
Character group of products      362—365 I
Character group of quotient group      365 I
Character group of R      367 I
Character group of T      366 I
Character group of weak direct product      364 I
Character group of Z      366 I
Character group with only one element      350 I 370
Character group, $\Delta$ -topology of      360 I
Character group, P-topology of      361 I
Character group, topologically isomorphic with the group      422 I
Character of a measure space      215 I
Character of a measure space and dimension of $\mathfrak{L}_2$       225 I
Character of a representation      13
Character(s) (of a group)      345 I
Character(s), $\lambda$ -measurable implies continuous      346 I

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