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Rudin W. — Fourier Analysis on Groups
Rudin W. — Fourier Analysis on Groups

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Название: Fourier Analysis on Groups

Автор: Rudin W.

Аннотация:

In the late 1950s, many of the more refined aspects of Fourier analysis were transferred from their original settings (the unit circle, the integers, the real line) to arbitrary locally compact abelian (LCA) groups. Rudin's book, published in 1962, was the first to give a systematic account of these developments and has come to be regarded as a classic in the field. The basic facts concerning Fourier analysis and the structure of LCA groups are proved in the opening chapters, in order to make the treatment relatively self-contained.


Язык: en

Рубрика: Математика/Анализ/Продвинутый анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1980

Количество страниц: 291

Добавлена в каталог: 08.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian group      252
Absolutely continuous      266
Adjoint      259
Affine maps      78
Almost periodic      32
Analytic type      197
Annihilator      35
Archimedean order      194
Asymmetry      104
Baire theorem      251
Base      248
Bochner's theorem      19
Bohr compactification      30
Borel function      267
Borel set      265
Bounded order      255
C-set      169
Cantor set      99
Cartesian product      251
CHARACTER      6
Closed graph theorem      258
Compact      248
Complete direct sum      37 254
Complex homomorphism      262
Component      249
Conjugate function      216
Connected      249
Continuous map      248
Continuous measure      266
Convolution      3 13
Coset      59 263
Coset ring      60
Cyclic group      253
Direct sum      37 254
Direct sum theorem      255
Discrete measure      266
Discrete topology      247
Divisible group      44
Domain transformation      131
Dual group      7
Dual space      257
E-function      121
Equivalent norms      258
Finite intersection property      24
Fubini's theorem      269
Gelfand topology      263
Gelfand transform      263
Generators      253
Geometric mean      203
Graph      81
Hadamard set      126
Hahn — Banach theorem      267
Half space      225
Hausdorff space      248
Helson set      114
Hilbert space      260
Homeomorphism      249
Homomorphism      252 262
I-group      46
Ideal      261
Independent sets      97
INDEX      253
Inner function      210
Inner product      260
Inversion theorem      22
Invertible      261
Irreducible indempotent      60
Isomorphism      252
Jordan decomposition      266
Kernel      252
Kronecker set      97
LCA      1
Lebesgue decomposition      66 198 266
Lexicographic order      194
Locally compact      248
Lusin's theorem      268
Maximal ideal      201
Maximal ideal space      263
Maximal semigroup      195
Mean value      118
Monothetic group      39
Natural homomorphism      253
Neighborhood base      248
Norm      257
Norm topology      257
Normalized Haar measure      24
Normed linear space      256
One-parameter subgroup      47
Open map      249
Order      194 253
Ordered group      194
Orthogonal      261
Orthogonality relations      10
Outer function      210
Parseval formula      27
Perfect set      99
Piecewise affine map      78
Plancherel transform      26
Pontryagin duality      28
Positive-definite      17
Product measure      269
Product space      251
Pseudo-periods      66
Quotient algebra      262
Quotient group      253
Quotient norm      257
Quotient space      257
Radon — Nikodym theorem      268
Range transformation      131
Real-analytic      132
Regular ideal      262
Regular measure      265
Relative topology      248
Restriction of a measure      256
Riesz representation theorem      266 267
Ring of sets      60
S-set      158
Schwarz inequality      261
Self-adjoint      104
Semi-simple      263
Semigroup      193
Separating      249
Sidon sets      120
Singular measure      266
Singular subgroup      60
Slowly oscillating      163
Spectral norm      264
Spectral radius      264
Spectrum      184 264
Stone — Weierstrass algebra      239
Stone — Weierstrass theorem      250
Support      250
Support group      1
Symmetric set      254
Tietze's extension theorem      250
Topological product      251
Topological space      247
topology      247
Total variation      265
Totally disconnected      249
translate      3
Translation lemma      66
Translation-invariant      1
Trigonometric polynomial      24
Tychonoff theorem      251
Uniform continuity      25
UNIT      261
Unit ball      257
Weak topology      249
Weak* topology      258
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