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Hewitt E., Ross K.A. — Abstract Harmonic Analysis (Vol. 1)
Hewitt E., Ross K.A. — Abstract Harmonic Analysis (Vol. 1)



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Название: Abstract Harmonic Analysis (Vol. 1)

Авторы: Hewitt E., Ross K.A.

Аннотация:

Abstract theory remains an indispensable foundation for the study of concrete cases. It shows what the general picture should look like and provides results that are useful again and again. Despite this, however, there are few, if any introductory texts that present a unified picture of the general abstract theory.A Course in Abstract Harmonic Analysis offers a concise, readable introduction to Fourier analysis on groups and unitary representation theory. After a brief review of the relevant parts of Banach algebra theory and spectral theory, the book proceeds to the basic facts about locally compact groups, Haar measure, and unitary representations, including the Gelfand-Raikov existence theorem. The author devotes two chapters to analysis on Abelian groups and compact groups, then explores induced representations, featuring the imprimitivity theorem and its applications. The book concludes with an informal discussion of some further aspects of the representation theory of non-compact, non-Abelian groups.


Язык: en

Рубрика: Математика/Анализ/Продвинутый анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1979

Количество страниц: 519

Добавлена в каталог: 02.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$mathfrac{D}(n)$      7
$mathfrac{D}(n)$ is compact      29
$mathfrac{D}(n)$ is locally Euclidean      29 —31
$M_a$      269
$M_a$ has approximate unit      303
$M_a$ has no unit      303
$M_a$, commutative if and only if G is      302
$M_a$, ideals characterized      303
$M_a$, isomorphic with $\mathfrak{L}_1$      272
$\alpha$-mesh      13
$\delta$-topology      360
$\Delta_a$      109 416—417
$\Delta_a$, character group of      402
$\Delta_a$, Haar measure on      202
$\Delta_p$      109
$\Delta_p$, automorphism group of      434
$\Delta_p$, minimal divisible extension of      419
$\iota$-almost everywhere      124
$\iota$-measurable function      125
$\iota$-measurable set      125
$\iota$-null function      124
$\iota$-null set      124
$\matfrak{G}\matfrak{L}(n, F)$      7
$\matfrak{G}\matfrak{L}(n, F)$ has inequivalent uniform structures      28—29
$\matfrak{G}\matfrak{L}(n, F)$ is locally Euclidean      29—31
$\matfrak{G}\matfrak{L}(n, F)$, Haar measure on      201 209
$\matfrak{G}\matfrak{L}(n, F)$, left invariant metric on      78
$\mathbb{Q}$ (rational numbers)      3
$\mathbb{Q}$, character group of      404 414
$\mathbb{R}$ (real line)      3
$\mathbb{R}$ is open continuous homomorph of totally disconnected group      50
$\mathbb{R}$, automorphism group of      433
$\mathbb{R}$, character group is R      367
$\mathbb{R}$, compact connected topology for      415
$\mathbb{R}$, continuous homomorphisms of      370
$\mathbb{R}$, Haar measure on      198
$\mathbb{R}$, invariant mean for $\mathfrak{U}(R)$      256
$\mathbb{R}$, invariant means for $\mathfrak{B}^r(R)$      240
$\mathbb{R}$, topologies in      27
$\mathbb{R}^n$      3
$\mathbb{R}^n$, automorphism group of      434
$\mathbb{R}^n$, characterized      104
$\mathbb{R}^n$, closed subgroups of      92
$\mathbb{Z}$ (integers)      3
$\mathbb{Z}$, character group is T      366
$\mathbb{Z}$, invariant mean for $\mathfrak{U}(Z)$      256
$\mathbb{Z}$, nondiscrete topology for      27
$\mathfrak{G}_0^{\ast}(G)$ as convolution algebra      265
$\mathfrak{G}_0^{\ast}(G)$, adjoint operation in      299
$\mathfrak{G}_0^{\ast}(G)$, equivalent with M{G)      269
$\mathfrak{G}_{00}(G)$      119
$\mathfrak{G}_{00}(G)$, nonnegative linear functionals on      120
$\mathfrak{G}_{00}(G)$, unbounded linear functionals on      167
$\mathfrak{L}_1(G)$, isomorphic with $M_a$      272 (see also “M_a(G)$”)
$\mathfrak{S}\mathfrak{D}(n)$      7
$\mathfrak{S}\mathfrak{D}(n)$ is compact      29
$\mathfrak{S}\mathfrak{D}(n)$ is locally Euclidean      29—31
$\mathfrak{S}\mathfrak{L}(n, F)$      7
$\mathfrak{S}\mathfrak{L}(n, F)$ has inequivalent uniform structures      28—29
$\mathfrak{S}\mathfrak{L}(n, F)$ has no finite-dimensional unitary representations      350
$\mathfrak{S}\mathfrak{L}(n, F)$ is locally Euclidean      29—31
$\mathfrak{S}\mathfrak{L}(n, F)$, homomorphisms into $[0,\infty]$      212—213
$\mathfrak{S}\mathfrak{U}(n)$      7
$\mathfrak{S}\mathfrak{U}(n)$ is compact      29
$\mathfrak{S}\mathfrak{U}(n)$ is locally Euclidean      29—31
$\mathfrak{U}(G)$      247
$\mathfrak{U}(G)$, existence of invariant means      250
$\mathfrak{U}(G)$, uniqueness of invariant means      252
$\mathfrak{U}(n)$      7
$\mathfrak{U}(n)$ is arcwise connected      64
$\mathfrak{U}(n)$ is compact      29
$\mathfrak{U}(n)$ is locally Euclidean      29—31
$\omega$-functions      259
$\Omega_a$      108
$\Omega_a$, character group of      400
$\Omega_a$, closed subgroups of      116
$\Omega_a$, Haar measure on      202—203
$\Omega_r$      109
$\Omega_r$, automorphism group of      433
$\Omega_r$, character group is $\Omega_r$      400
$\sigma$-algebra of sets      118
$\sigma$-compact spaces      11
$\sigma$-compact spaces, products of      13—14
$\sigma$-finite set function      118
$\sigma$-locally finite      13
$\sigma$-ring of sets      118
$\sim$-representation      314
$\varepsilon$-mesh      13
0-dimensional group, small subgroups of      62
0-dimensional space      11
a-adic integers      109 (see also “$A_a$”)
a-adic numbers      109 (see also “$Q_a$”)
a-adic solenoid      114
Abe, M.      425 439
Abelian group, nondiscrete topologies      27 (see also “Group”)
Absolutely continuous measure      180 269
Additive function      452
Adjoint homomorphism      392
Adjoint in $\mathfrak{B}^{\ast}(G)$      310
Adjoint in $\mathfrak{B}^{\ast}_u(G)$      310
Adjoint in an algebra      313
Adjoint in M(G)      300
Adjoint n $\mathfrak{G}^{\ast}_0(G)$      299
Adjoint operator      466
Alaoglu’s theorem      458
Aleksandrov, A.D.      215
Aleksandrov, P. S.      47 386
Alexander, J.W.      78 354 398
Algebra      469
Algebra $\sim$-algebra      313
Algebra , convolution      263
Algebra homomorphism      470
Algebra imbedded in algebra with unit      470
Algebra of sets      118
Algebra with adjoint operation      313
Almost everywhere      124
Almost periodic function      247 (see also “$\mathfrak{U}(G)$”)
Annihilator      365
Anzai, H.      399 425 439
Approximate unit      303
Approximation theorems      431—432 435
Arbitrarily small sets      62
Arcwise connected space      11
Arens, R.F.      439
Arhangel’skii, A.      398
Aronszajn, N.      465
Aubert, K. E.      214
Automorphism group      426—429
Automorphism group, examples      433
Automorphism group, inner automorphism subgroup      439
Automorphism group, modular function of      438
Automorphism group, non locally compact      435
Automorphism, inner      4
Automorphism, topological      426 208
Baer, R.      31 51
Baire category theorem      42 456
Baire measurable function      118
Baire sets      118
Baire sets and Haar measure      280
Balanced neighborhood      453
Balcerzyk, S.      425
Banach $\sim$-algebra      313
Banach algebra      469
Banach fields, characterized      473
Banach space      455
Banach space, reflexive      457
Banach space, weak topology      458
Banach space, weak-$\ast$ topology      458
Banach — Steinhaus theorem      456
Basis of a group      442
Basis of a measure space      215
Basis, orthonormal      465
Beaumont, R.A.      425
Beurling, A.      261 282
Bilinear functional      453
Bilinear functional, bounded      468
Birkhoff, G.      83 243 461
Bochner, S.      1 282
Bohr compactification      430
Borel measurable function      118
Borel sets      118
Bounded bilinear functional      468
Bounded linear function      454
Bounded linear function, relatively      46l
Bounded order      439
Bounded order, characterized      449
Bourbaki, N.      32 46 52 134 135 150 166 184 461
Braconnier, J.      56 60 208 278 373 395 396 398 399 417 425 426 438
Buck, R.C.      275 283
Bunyakovskii’s inequality      137
Bunyakovskii’s inequality, characterized as Banach algebra      481
Bunyakovskii’s inequality, closed ideals in      482
Bunyakovskii’s inequality, conjugate space of      170 175
Bunyakovskii’s inequality, multiplicative linear functionals of      483
Bunyakovskii’s inequality, structure space is X      483
Calderon, A. P.      261
Cancellation laws      98—99
Cancellation semigroup      258
Caratheodory outer measure      123
Cardinal number of character groups      382 396
Cardinal number of nondiscrete locally compact groups      31
Cardinal number, notation for      2
Cartan, E.      32
Cartan, H.      57 135 214 283 398
Cartesian product of sets      2
Category, Baire      456
Category, theorem of Baire      42 456
Cauchy — Bunyakovskii — Schwarz inequality      464
Cauchy’s inequality      137
Center of a topological group      46 64 429
Character group      355
Character group and structure space of $M_a(G)$      358 360 361
Character group of $Q_d$      404 414
Character group of $R_d$      405
Character group of $T_d$      405
Character group of $Z(a^{\infty})$      402—403
Character group of $\Delta_a$      402
Character group of $\Omega_a$      400
Character group of $\Sigma_a$      403
Character group of closed subgroup      380
Character group of finite group      367
Character group of local direct product      373
Character group of products      362—365
Character group of quotient group      365
Character group of R      367
Character group of T      366
Character group of weak direct product      364
Character group of Z      366
Character group with only one element      350 370
Character group, $\Delta$-topology of      360
Character group, P-topology of      361
Character group, topologically isomorphic with the group      422
Character of a measure space      215
Character of a measure space and dimension of $\mathfrak{L}_2$      225
Character(s)      345
Character(s), $\lambda$-measurable implies continuous      346
Character(s), extensibility of      380
Character(s), product of      355
Character(s), real      390 393
Character(s), sufficiently many      345
Characteristic function      2
Chevalley, C.      67 106 214
Cluster point of a net      14
Cofinal set      2
Cohen, L.W.      78
Cohen, P.J.      184
Commutative algebra      469
Commutator subgroup      358
Compact elements      92 103
Compact groups have discrete character groups      362
Compact groups, algebraic structure of Abelian      410—414
Compact groups, small subgroups      61—62
Compact groups, torsion characterized      406
Compact groups, torsion-free characterized      406
Compact space      11
Compactification, Bohr      430
Compactly generated group      35
Complete lattice      462
Complete measure space      216
Complete regularity of groups      70
Completely regular space      9
Completely simple semigroup      101
Complex algebra      469
Complex linear space      452
Complex measure(s)      118
Complex measure(s), Fubini’s theorem for      183
Complex measure(s), product of      182
Complex n-dimensional space      3
Component      11
Component of e as direct factor      395
Component of e in topological groups      60—63
Composition of functions      2
Concentrated a measure      180
Conjugacy classes of a group      5
Conjugate elements of a group      5
Conjugate of a matrix      7
Conjugate space      457
Conjugate space of $\mathfrak{G}_0$      170 175
Conjugate space of $\mathfrak{L}_p$      148
Conjugate-linear function      452
Connected groups      62 383 385 390 410
Connected groups, center of      64 429
Connected space      11
Continuous measure      269 132
Continuous representation      341
Continuous representation, strongly      335
Continuous representation, weakly      335
Continuous unitary representations, equivalences      346
Convergent net      14
Convex combination      452
Convex set      452
Convex set in ordered group      25
Convolution      262
Convolution algebra      263
Convolution algebra, $l_1(S)$      263
Convolution algebra, $\mathfrak{B}^{\ast}(S)$      275
Convolution algebra, $\mathfrak{G}^{\ast}_0(S)$      265
Convolution algebra, $\mathfrak{G}^{\ast}_{lu}(S)$ and $\mathfrak{G}^{\ast}_{ru}(S)$      275
Convolution algebra, noncommutative      275—276
Convolution of functions and measures      286 290—298
Convolution of measures      266—269
Convolution, associativity of      262
Convolution, involving unbounded functionals      278
Convolution, using right Haar measure      306
Correspondence      2
Corson, H.H.      81
Cotlar, M.      375
Countable set      2
Countably additive measure      118
Countably compact space      11
Covering (cover)      2
Cyclic groups, finite      5
Cyclic representation      315
Cyclic vector      315
Daniell, P. J.      134
Dantzig, D. van      32 51 67 78 83 117 425
Daublebsky von Sterneck, R.      282
Davis, H.F.      215
Day, M.M.      238 241 245 372
Devinatz, A.      399
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