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

Character(s), extensibility of      380 I
Character(s), product of      355 I
Character(s), sufficiently many      345 I
Character, real      390 I 393
Characteristic function      2 I
Clebsch — Gordan series      154
Clebsch, A.      154
Closed under operations x and conjugation      21
Cluster point (of a net)      14 I
Coefficient operators      329
Cofinal set      2 I
Cohen, P. J.      290
Cohen’s factorization theorem      268
Coifman, R. R.      679
Collins, H. S.      290
Commutative algebra      469 I
Commutator subgroup      358 I 142
Compact elements      92 I 103
Compact groups have discrete character groups      362 I
Compact groups with no small subgroups      101 194
Compact groups, algebraic structure of Abelian      410—414 I
Compact groups, small subgroups      61—62 I 302
Compact groups, torsion characterized      406 I
Compact groups, torsion-free characterized      406 I
Compact space      111
Compactification, Bohr      403 I 302
Compactly generated group      35 I
Complete lattice      462 I
Complete measure space      216 I
Complete regularity of groups      70 I
Complete tensor product      578
Completely regular space      9 I
Completely simple semigroup      101 I
Complex algebra      469 I
Complex linear space      452 I
Complex measures      118 I
Complex measures, Fubini’s theorem for      183 I
Complex measures, product of      182 I
Complex n-dimensional space      3 I
Component      111
Component of e as direct factor      395 I
Component of e in topological groups      60—63 I
Composition of functions      2 I
Concentrated (a measure)      180 I
Condon, E. U.      154
Conjugacy classes of a group      5 I
Conjugate elements of a group      5 I
Conjugate equivalence class      17
Conjugate function of $\varphi$       702
Conjugate of a matrix      7 I
Conjugate representation      17 58
Conjugate space      457 I
Conjugate space of $\mathfrak{G}_0$       470 I 175
Conjugate space of $\mathfrak{G}_p$       74
Conjugate space of $\mathfrak{L}_p$       148 I
Conjugate-linear function      452 I
Conjugation on Hilbert space      15
Connected groups      62 I 383 385 390 410 69
Connected groups, center of      65 I 429
Connected space      111
Continuous measure      269 I 132
Continuous representation      341 I
Continuous representation, strongly      335 I
Continuous representation, weakly      335 I
Continuous unitary representations, equivalences      346 I
Contragredient representation      60
Convergent net      14 I
Convex combination      452 I
Convex set      452 I
Convex set in ordered group      25 I
Convolution      262 I
Convolution algebra      263 I
Convolution algebra $\mathfrak{B}^{\ast}(S)$       275 I
Convolution algebra,       263 I
Convolution algebra, $\mathfrak{G}(G)$       84
Convolution algebra, $\mathfrak{G}^{ast}_{0}(G)$       265 I
Convolution algebra, $\mathfrak{G}^{ast}_{lu}(G)$ and $\mathfrak{G}^{ast}_{ru}(G)$       275 I
Convolution algebra, $\mathfrak{L}_p(G)$       84
Convolution algebra, noncommutative      275—276 I
Convolution of functions and measures      286 I 290—298
Convolution of measures      266—2691
Convolution, associativity of      262 I
Convolution, involving unbounded functionals      278 I
Convolution, using right Haar measure      306 I
Coordinate functions      3
Coordinate functions, orthogonality relations      11
Correspondence      2 I
Countable set      2 I
Countably additive measure      118 I
Countably compact space      111
Courant, R.      153
Covering (cover)      2 I
Craw, I. G.      290
Curtis, C. W.      103
Curtis, P. C. Jr.      284 286 290
CYCLE      45
Cyclic groups, finite      5 I
Cyclic representation      315 I
Cyclic vector      315 I
D"-sequence      637
D'-sequence      637
D-sequence      637
de Leeuw, K.      290 310 414 605
Decomposition of representations      19
Decomposition of representations, uniqueness of      19 29 40
Dedekind, R.      483
Dels arte, J.      551
Derivative with respect to $\mu$       653
Dieudonne, J.      495
Difference space      452 I
Dihedral group       51
Dihedral group , dual object of      55
DIMENSION      15 I
Dimension of a Hilbert space      465 I
Direct product of groups      6 I
Direct product of topological groups      52 I
Direct product, character group of      362—365 I
Direct product, dual object of      27
Direct product, local      56—57 I
Direct product, weak      6 I
Direct sum of Hilbert spaces      468 I
Direct sum of linear spaces      452 I
Direct sum of matrices      691
Direct sum of operators      688
Direct sum of representations      18
Directs (directed set)      14 I
Discontinuous measure, purely      269 I
Discrete group      24 I
Discrete group has compact character group      362 I
Discrete group, Haar measure on      198 I
Dissociate set      425
Ditkin sets      604
Ditkin, V. A.      253 506 519 520
Ditkin’s condition      497
Ditkin’s condition for $\mathfrak{L}_1(G)$       501
Ditkin’s condition for $\mathfrak{R}(G)$       344
Ditkin’s condition for modules in $\mathfrak{L}_1$       504
Ditkin’s theorem      497
Ditkin’s theorem, generalized      515
Divisible group      440 I 66
Divisible group, characterized      444 I
Divisible group, imbeddings in      445—447 I
Divisible group, torsion-free characterized      421 I
Dixmier, J.      114 289 291 521 602
Domain of transitivity      46
Domar, Y.      521 550
Dominated Convergence Theorem      181—182 I
Doss, R.      232
Douady, A.      365
Dual group      355 I (see also “Character group”)

Dual object(s)      2
Dual object(s) is not a group      37
Dual object(s) of $\mathfrak{D}(3)$       151 ’
Dual object(s) of $\mathfrak{S}\mathfrak{D}(3)$       140—141
Dual object(s) of $\mathfrak{S}\mathfrak{U}(2)$       135 136
Dual object(s) of $\mathfrak{U}(2)$       150
Dual object(s) of direct product      27
Dual object(s) of finite groups      54
Dual object(s) of quotient groups      65
Dual object(s), closed under operations      21
Dual object(s), isomorphic      21 57
Dual object(s), tensor product in      21
Duality theorem, Abelian      378 I
Duality theorem, Tannaka — Krein      156—189
Duality theorem, uniqueness of T      424 I
Dunford, N.      114 326 543
Eberlein — Schoenberg theorem      304
Eberlein, W. F.      327
Edwards, R. E.      115 217 250 290 291 327 413 414 415 430 434 441 515 516 520 549 669 679
Elliott, R. J.      551
Empty set      2 I
Equidistributions      432 I 437
Equivalent representations      314 I 2
Equivalent uniform structures      21 I
Ernest, J.      113 208
Essentially bounded functions      141 I
Euler, L.      156
Euler’s angles      137
Exponential of a matrix      29 I
Extensibility of characters      380 I
Extensibility of real characters      391 I
Extensible positive functional      317 I
Extensions of Haar measure      216 I
Extensions of measure spaces      216 I
Extensions of representations      32
Extreme point      459 I
Extreme subset      459 I
Eymard, P.      290 365 367 522
F. Riesz’s representation theorem      129 I
F. Riesz’s representation theorem for Hilbert spaces      464 I
Factor      6 I
Factorization set      515
Factorization theorems      268 270 284 287
Factorization theorems in $\mathfrak{R}(G)$       337 354
Factorization theorems, $\mathfrak{L}_1\ast\mathfrak{G}=\mathfrak{G}$       272
Factorization theorems, $\mathfrak{L}_1\ast\mathfrak{G}_0=\mathfrak{G}_0$       283
Factorization theorems, $\mathfrak{L}_1\ast\mathfrak{L}_p=\mathfrak{L}_p$       271
Fejer, L.      679
Fekete, M.      412 413
Fell, J. M. G.      60
Fever’s kernel      216 239 672
Field of scalars      452 I
Figa — Talamanca, A.      147 152 153 284 286 290 385 414 415 435 437 447
Filippi, M.      604
Finite cyclic groups      5 I
Finite intersection property      2 I
Finite-dimensional representation, direct sum of irreducibles      333—334 I
Finite-dimensional representation, no unitary      348—351 I
Finitely additive measures      118 I
Finitely additive measures, invariant      242—245 I
Finitely generated group      449 I
Finitely generated group, characterized      451 I
First category      456 I
First isomorphism theorem for groups      5 I
First isomorphism theorem for topological groups      44 I
Fischer, E.      251
Ford, C.      70
Fourier series      329
Fourier series, absolutely convergent      330
Fourier transform      359 I 478 78
Fourier transform on subgroups and quotient groups      242
Fourier transform, $\mathfrak{L}_2$       225
Fourier transform, $\mathfrak{L}_p$       227
Fourier transform, inverse      210 228 351
Fourier — Stieltjes series      329
Fourier — Stieltjes transform      359 I 78
Fourier — Stieltjes transform, characterized      304 359
Fourier — Stieltjes transform, inverse      210
Free Abelian group      8 I
Free group      8 I
Free topological group      72 I
Frobenius reciprocity theorem      462
Frobenius, G.      59 60 483 693
Fubini’s Theorem      153—1561
Fubini’s theorem for complex measures      183 I
Fukamiya, M.      521
Function of positive type      253
Functional, bilinear      453 I
Functional, bounded bilinear      468 I
Functional, conjugate-linear      452 I
Functional, linear      452 I
Functional, multiplicative linear      474 I
Functional, nonnegative      461 I
Functional, positive      316 I
Functional, relatively bounded      461 I
Functional, strictly positive      46l I
Functional, total variation of      168 I
Functions operating in algebras      490 603
Fundamental theorem of Abelian groups      451 I
Gaposkin, V. F.      449
Garsia, A. M.      550
Gaudry, G. I.      361 414 434
Gel’fand topology      478 I
Gel’fand — Mazur theorem      473 I
Gel’fand — Raikov theorem      343 I
Gel’fand, I. M.      154 155 289 290 325 326 518 519 520 602
Gel’fand’s theorem      478 I
General linear group      7 I (see also “ $$\mathfrak{B}\mathfrak{L}(n</a></span> <span class=subjpages><a href=$ F)$"/>”)
Generalized quaternion group       52
Generalized quaternion group , dual object      57
Generator of monothetic group      105 I 407 415
Gilbert, J. E.      327 551 552 604 605
Gillman, L.      518
Glaeser, G.      605
Glicksberg, I.      143 290 310 312
Godement, R.      114 156 250 251 252 289 309 310 325 326 327 521 538 545 550 602
Goldberg, R. R.      520
Gordan, P.      154
Graev, M. I.      155
Grothendieck, A.      414 415
Group      see “Topological group”
Group (=Abelian group in Appendix A)      4391
Group of bounded order      439 I
Group, bounded order characterized      449 I
Group, divisible      440 I 66
Group, finite cyclic      5 I
Group, finitely generated      449 I
Group, free      8 I
Group, free abelian      8 I
Group, linear      7 I
Group, p-primary      439 I
Group, permutation      8 I
Group, reduced      440 I
Group, solvable      142
Group, symmetric      8 I
Group, topological      see “Topological group”
Group, torsion      439 I
Group, torsion-free      439 I
Grunwald, G.      446
Gurevic, A.      60
Haar integral (left)      184—194 I (see also “Haar measure”)
Haar integral, examples of      198 I 209
Haar integral, existence and uniqueness of      185—193 I
Haar integral, right      195 I
Haar measure (left)      194 I 210
Haar measure and Baire sets      280 I
Haar measure, examples of      198 I 209
Haar measure, extensions of      216 I
Haar measure, right      195 I
Haar measure, uniqueness of      193—194 I 313

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