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

Measure(s), total variation of      169 I
Mela, J. F.      576
mesh      13 I
Metrizability of topological groups      70 I
Meyer, Y.      547 603 605
Milnor, J. W.      207
Minimal divisible extension of a group      419 I 445—447
Minkowski’s inequality      138 I
Mirkil, H.      603
Modular function      196 I
Modular function for $\mathfrak{S}(G)$       438 I
Modular function on closed normal subgroups      206 I
Monothetic group      85 I 390 407—409
Monothetic group, generators of      105 I 407 415
Monothetic group, largest      407 I
Monothetic semigroups      105 I
Moore, J. C.      208
Morgenthaler, G. W.      446
Mostow, G. D.      198 205 207
Mrowka, S.      99
Multilinear mapping      722
Multinomial coefficient      117
Multiplicative function      345 I
Multiplicative linear functional      474 I
Multiplicity of family of sets      15 I
Multiplicity of representations      18
Multipliers      368
Multipliers, isometric      389
Multipliers, table of      410—411
Murakami, S.      60
Murnaghan, F. D.      155
Mycielski, J.      69
n-dimensional space      3 I 15
Nagumo, M.      518
Naimark, M. A.      154 207 251 252 290 325 326 327 495 520
Nakamura, M.      325
Nakayama, T.      113 208 483
Namioka, I.      710
Narrow topology      549
Natural mapping      4 I
Neighborhood (always open)      9 I
Net      14 I
Neumann, J. von      60 113 114 290 312 322 323 326 366 518 549 574 680 693
Noble, M. E.      448
Nondiscrete topologies for Abelian groups      27 I
Nondiscrete topologies for Z      27 I
Nonmeasurable sets      226 I
Nonnegative linear functional      461 I
Nonnegative linear functional on $\mathfrak{C}_{00}$       120 I
Nonnormal groups      74—76 I
Norm      453 I
Norm in       3 I
Norm in       3 I
Norm in $\mathfrak{L}_p(X,\iota)$       135 I
Norm of linear function      454 I
Norm of multilinear mapping      722
Norm topology      454 I
Norm,      703
Norm, uniform      119 I 230
Normal algebra      484
Normal family of functions      495
Normal operator      467 I
Normal operator, existence of inverse      484 I
Normal subgroup      16 I
Normal topological group      16 I
Normality of locally compact groups      761
Normed $\sim$ -algebra      313 I
Normed A -module      263
Normed algebra      469 I
Normed linear space      453 I
Normed linear space, reflexive      457 I
Normed linear space, weak topology      458 I
Normed linear space, weak- $^{\ast}$ topology      458 I
Nowhere dense      456 I
Null function      124 I
Null set      124 I
Nyman, B.      521
Oberhettinger, F.      214
One-parameter subgroup      85 I
Open and closed subgroup      33—34 I 62
Open mapping theorems      710
Operations $\Omega$       180
Operators      452 I
Operators, adjoint      466 I
Operators, direct sum of      688
Operators, Hermitian      467 I
Operators, normal      467 I
Operators, positive-definite      467 I
Operators, projection      467 I
Operators, sublinear      631
Operators, sum of      468 I
Operators, unitary      467 I
Orbit      46 311
Ordered groups      24 I
Orlicz, W.      413
Orthogonal elements      465 I
Orthogonal group      7 I (see also “\mathfrak{D}(n)$”)
Orthogonal group, special      7 I (see also ““\mathfrak{S}\mathfrak{D}(n)$”)
Orthogonal matrix      7 I
Orthogonal set      465 I
Orthogonal sets      465 I
Orthogonality relations in $\mathfrak{T}(G)$       8 11 14
Orthonormal basis      465 I
Orthonormal set      465 I
Ovaert, J.-L.      290
p-adic integers      109 I (see also “ $\Delta_p$ ”)
p-adic number field      112 I (see also “ $\Omega_r$ ”)
p-adic numbers      109 I (see also “ $\Omega_r$ ”)
p-primary group      439 I
p-rank of a group      444 I
P-topology      361 I
Paley, R. E. A. C.      413 414
Paracompact space      13 I
Paracompactness of locally compact groups      76 I
Parker, W. A.      448
Parseval, M. A.      250
Parseval’s identity      226
Parseval’s identity, generalizations      249
Partition of a set      2 I
Partitions of unity      9 —10 I 495
Permutation group      8 I
permutations      8 I
Permutations, transitive      46
Peter — Weyl theorem      24 81
Peter, F.      60 114 366 548
Phillips, K. L.      679
Phillips, R. S.      327
Pitt, H. R.      511 519 520 574
Pitt’s Tauberian theorems      511
Plancherel, M.      251 252
Plancherel’s theorem      226
Poisson summation formula      246
Pollard, H.      549 550
Pontryagin — van Kampen duality theorem      378 I
Pontryagin — van Kampen duality theorem, uniqueness of T      424 I
Positive functionals      316 I
Positive functionals on $\mathfrak{L}_p$       357
Positive functionals, continuity of      270 274
Positive functionals, discontinuous      357
Positive functionals, extensible      317 I
Positive functionals, nonextensible      331 I
Positive linear functional, strictly      461 I
Positive-definite functions      253 161
Positive-definite functions, 1-integrally      275
Positive-definite functions, decomposition theorem      260
Positive-definite functions, extensions      363
Positive-definite functions, p-integrally      290
Positive-definite functions, pointwise limits of      280 288 301 302
Positive-definite matrix      683
Positive-definite operator      467 I

Positive-definite operator, spectrum is nonnegative      484 I
Positive-definite operator, square root of      485 I 691
Pospisil, B.      99
POVZNER, A.      251 325 550
primary group      439 I
Product of characters      355 I
Product of complex measures      182 I
Product of functionals      152 I 159
Product of groups      6 I
Product of measures 1      52 I
Product of sets      2—3 I
Product of topological groups      52 I
Product of topological groups, character group of      362—365 I
Projection      54 I
Projection operator      467 I
Projection-valued measure      316
Projective limit      56 I
Projective limit, compact groups      102
Proper ideal of an algebra      469 I
Proper subgroup      4 I
Property       480
Property       481
Pseudomeasures      361
Pure independent set      448 I
Pure subgroups      447 I 395
Purely discontinuous measure      269 I
Quasi-inverses      471 I
Quasi-inverses, form open set      472 I
Quaternion group      52 (see also “Generalized quaternion group $Q_m$

”)
Quaternions of norm      1 I52
Quaternions, Haar measure on      210 I
Quotient group      4 I 40
Quotient group, character group of      365 I
Quotient space      4 I 452
Quotient space, homogeneity of      37 I
Quotient space, topology of      36 I
r-adic integers      109 I (see also “ $\Delta_p$ ”)
r-adic numbers      109 I (see also “ $\Omega_r$ ”)
r-iold transitive      46
RAAA      preface
Radon — Nikodym theorem      144 I
Raikov, D. A.      289 290 291 325
Rajagopalan, M.      448 469
Rank of a group      444 I
Rao, M. M.      252
Real algebra      469 I
Real characters      390 I 393
Real characters, extensibility of      391 I
Real linear space      452 I
Real matrix      7 I
Real n-dimensional space      3 I
Real-character group      390 I
Reduce      323 I
Reduced group      440 I
Reduced word      8 I
Reducible representation      323 I
Reducible set of operators      323 I
refinement      13 I
Reflexive space      457 I
Regular algebra      484
Regular ideal      475 I
Regular left ideal      474 I
Regular measure      127 I
Regular representation      342 I 36 58 473
Regular topological space      9 I
Reiner, I.      103
Reiter, H. J.      327 433 517 520 533 539
Reiter’s theorem      529
Relatively bounded linear functional      461 I
Relatively invariant functionals      203 I
Relatively invariant functionals, examples      212 I
Representation space      312 I
Representation(s) of a group      312 I
Representation(s) of a semigroup      312 I
Representation(s) of an algebra      312 I
Representation(s) of an algebra with unit      313 I
Representation(s) of finite groups      47
Representation(s), character of      13
Representation(s), conjugate      17 58
Representation(s), contained in      18
Representation(s), continuous      341 I
Representation(s), cyclic      315 I
Representation(s), decomposition of      19
Representation(s), direct sum of      18
Representation(s), equivalent      314 I 2
Representation(s), extension of      29
Representation(s), identity      3
Representation(s), invariant subspace under      312 I
Representation(s), irreducible      323 I
Representation(s), multiplicity      18
Representation(s), reducible      323 I
Representation(s), regular      342 I 36 58 473
Representation(s), restriction of      29
Representation(s), strongly continuous      335 I
Representation(s), sufficiently many      343 I
Representation(s), summand of      18
Representation(s), tensor product of      20
Representation(s), weakly continuous      335 I
Representation(s), weakly measurable      335 I
Representative functions      5
Restriction algebra      485
Restriction of representations      29
Richards, I.      602
Rickert, N. W.      291 469 567
Rider, D.      147 152 153 414 415 442 447 448
Rieffel, M. A.      287 290 414
Riemann — Lebesgue lemma      81
Riesz products      426 448
Riesz — Thorin convexity theorem      722
Riesz — Thorin convexity theorem, applied      76 226—228
Riesz, F.      251 252 290 325 326 445 448
Riesz, M.      252 413
Right Haar integral      195 I (see also “Left Haar integral”)
Right Haar measure      195 I (see also “Left Haar measure”)
Right unit relative to I      474 —475 I (see also “Left unit relative to I”)
Ring of sets      118 I
Rolewicz, S.      576
Rosenthal, H. P.      437 576 604 605
Ross, K. A.      208 291 629 679
Rudin — Shapiro polynomials      429
Rudin, W.      238 250 251 252 253 290 326 327 429 437 446 447 448 513 533 548 552 570 574 576 602 603
Ryll — Nardzewski, C.      576
Saeki, S.      516 601
Sakai, S.      415
Saks, S.      218
Salem, R.      290 446 551 575 576 603 604
Sankaran, S.      325
Sapiro, Z. Ya.      154
Scalar field      452 I
Schatten, R.      113 683
Schoenberg, I. J.      327
Schur, I.      59 60 153 289 483
Schur’s lemma      6
Schwartz, J. T.      114 153 543
Schwartz, L.      253 533 551 602 603
Schwartz’s example      533
Schwarz’s inequality      464 I
Second category      456 I
Second character group      376 I
Second isomorphism theorem for groups      51
Second isomorphism theorem for topological groups      45 I
Sections      153 I
Segal, I. E.      60 114 290 430 447 483 521 548 602
Self-dual groups      422 I
Self-representation      47 115
Semicharacter      345 I
Semicontinuous functions      121 I
Semidirect product of groups      6—7 I
Semidirect product of topological groups      58 —59 I
Semidirect product, Haar measure on      210 I

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