Bachman G. — Elements of Abstract Harmonic Analysis :: Электронная библиотека попечительского совета мехмата МГУ

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Bachman G. — Elements of Abstract Harmonic Analysis

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Название: Elements of Abstract Harmonic Analysis

Автор: Bachman G.

Аннотация:

Abstract Harmonic Analysis is an active branch of modern analysis which is increasing in importance as a standard course for the beginning graduate student. Concepts like Banach algebras, Haar measure, locally compact Abelian groups, etc., appear in many current research papers. This book is intended to enable the student to approach the original literature more quickly by informing him of these concepts and the basic theorems involving them.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1964

Количество страниц: 266

Добавлена в каталог: 11.11.2013

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Предметный указатель

th power summable      1
-section      177
-section      177
$\sigma$ -algebra      125
Absolute continuity of a measure      245
Absolutely convergent trigonometric series, space of      26
Adherence point      62
Algebra, $\sigma$ -algebra      125
Algebra, Banach      25
Algebra, completely symmetric Banach      210
Algebra, of sets      125
Algebra, with involution (star, symmetric)      97 188
Analytic vector-valued function      29
Approximate identity      9 190
Banach algebra      25
Banach space      2
Basis at a point      73
Basis of open sets      73
Bicontinuous mapping      62
Bochner’s theorem      223 246
Borel complex-measure      211
Borel measure      126
Borel regular-measure      215
Borel sets      125
Bounded linear functional      29
Canonical mapping      110
Cartesian product (of topological spaces)      78-79 85
Cauchy integral formula      32
Cauchy integral theorem      31
Cauchy — Hadamard formula      32
Cauchy — Schwarz inequality      17
CHARACTER      193 200
Closed set      62
Closure      62
Cluster point      123
Compact      81
Compact, locally      85
Compactification, one-point      118
Content      163
Content, inner      164
Content, regular      164
Continuity, uniform      107
Continuous mapping      62
Continuous partition of the identity      121
Convergence in a topological space      123
Convergence of a generalized sequence      116
Convolution      6 180
Coset      50
Countability, first axiom of      73
Countability, second axiom of      74
Countably additive class      125
Covering      81
Covering, finite      81
Covering, open      81
Daniell extension      158 166
Directed set      116
Discrete topology      61
Dominated Convergence Theorem      16
Double integral      178
Dual group      193
Duality theorem      241
Essential supremum (ess sup)      196
Extended Stone — Weierstrass Theorem      244
Extension theorem (Tietze)      118
Factor group      114
Fatou’s Lemma      16
Finite intersection property      83
Fourier Transform on $L_{1}(-\infty, \infty)$       1 ff.
Fourier Transform on $L_{1}(G)$       207 ff. 210
Fourier Transform on $L_{2}(-\infty, \infty)$       19-20
Fourier Transform on $L_{2}(G)$       237
Fourier — Stieltjes transform      219 ff. 224
Fubini’s Theorem      16 179 213
Fundamental system of neighborhoods      74
Gel’fand theory      48 ff.
Gel’fand topology      87
Generalized Cauchy sequence      116
Generalized nilpotent element      57
Generalized sequence (convergence of)      116
Generated topology      77
Group, algebra      27
Group, dual      193
Group, factor      114
Group, general linear      99
Group, homogeneous      103
Group, quotient      114
Group, regular      106
Group, topological      98
Group, unimodular      99
H $\ddot{o}$ lder’s inequality      17
Haar covering function      130
Haar integral      128 129 172
Haar measure      126 169 172
Hausdorff space      80
Homeomorphism      62
Homogeneous      103
Ideal      48
Ideal, maximal      49
Ideal, principal      50
Ideal, proper      48
Identity, continuous partition of      121
Induced measure      128
Induced topology      78
Inner regular Borel measure; outer regular Borel measure      215
Interior point      71
Inversion formulas, $L_{1}(-\infty, \infty)$       5
Inversion formulas, $L_{1}(G)$       227
Inversion formulas, $L_{2}(-\infty, \infty)$       24
Involution, algebra with      97
Isomorphism      123

Iterated integral      178
Jordan decomposition theorem      212
Lattice, linear vector      159
Lebesgue point      5
Limit point      123
Liouville’s theorem      30
Locally compact      85
Lower semicontinuous function      166
Maximal ideal      49
Measurable function      128
Measurable set      168
Measurable transformation      127-128
Measurable, $\mu^{*}$       161
Measure, absolute continuity of      245
Measure, complex Borel      211
Measure, outer      64
Measure, product      176 ff.
Measure, signed      212
Minkowski inequality      17
Modular function      187
Natural mapping      110
Neighborhood      66 ff.
Neighborhood, fundamental system of      74
Neighborhood, symmetric      104
Neighborhood, topology      66 ff.
Nilpotent element      57
Normal space      117
Normal subgroup      110
Normed algebra      25
One-point compactification      118
Open mapping      111
Open sets      61
Open sets, in terms of neighborhoods      67
Outer measure      164
Parseval’s theorem      20 244
Plancherel’s theorem      24 235
Pontrjagin duality theorem      241
Positive definite function      220
Positive linear functional      158
Power set      61
Principal ideal      50
Product measures      176 ff.
Product space      78 79
Projection mapping      84
Proper ideal      48
Quotient algebra      50
Quotient group      114
Radical      56
Radon — Nikodym theorem      245
Regular content      163
Regular measure (inner, outer)      215
Regular point      37
Regular topological space      106
Relative topology      78
Representation theorem      160
Representation Theorem, Riesz      245
Resolvent operator      41
Riemann — Lebesgue lemma      4
Right Haar measure      126 172
Ring of sets      125
Semisimple      57
Separation axioms      79 ff.
Sigma$-bounded      164
Sigma$-ring      125
Simple function      217
Spectral radius      42
Spectrum of an element      37
Star (symmetric) algebra      97
Stone — Weierstrass theorem      244
Stronger topology      77
Subbasis (subbase)      75
Subgroup      109
Subgroup, closed      110
Subgroup, normal      114
Subspace topology      78
Summable set      168
Support of a function      107
Symmetric neighborhood      104
Tietze extension theorem      118
Tonelli — Hobson Theorem      17
Topological divisor of zero      53
Topological group      98
Topological group, homogeneous      103
Topological group, locally compact      107
Topological group, normal subgroup      114
Topological group, regular      106
Topological group, subgroup of      109
Topological space      61 ff.
topology      61
Topology, discrete      61
Topology, Gel’fand      87
Topology, generated      77
Topology, induced      78
Topology, relative (subspace)      78
Topology, trivial      61
Topology, Tychonoff      85
Topology, weak      78
Topology, weaker (stronger)      77
Total variation      211
Tychonoff theorem      85
Tychonoff topology      85
Uniformly continuous      107
Unimodular group      99
UNIT      34
Urysohn’s lemma      118
Weak topology      78
Weaker topology      77
Wiener theorem      60
Zero set      167
Zorn’s Lemma      49

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