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Электронная библиотека Попечительского совета
механико-математического факультета
Московского государственного университета
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| Loomis L.H. - An introduction to abstract harmonic analysis |
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| Предметный указатель |
 algebra 28
algebra, commutative algebra 88 91
 algebra 100 27
 -bounded function 33
-monotone family 33
 -norm 37 46
 -space 37 14
-space, complex -space 46
 -space 111
Absolute continuity 40
Adjoint 21
Adverse 64
Algebra 8; see 'Banach algebra'
Algebra, Banach algebra 16 48
Algebra, function algebra 53
Algebra, group algebra 123
Almost invariant function 160
Almost periodic function 165 41
Analytic function theorem 78
Annihilator 20
Approximate identity 124
Axiom of Choice 2
Baire function 32
Banach algebra 16 48
Banach algebra, algebra 28 88 91
Banach algebra, algebra 100
Banach algebra, regular Banach algebra 82
Banach algebra, self-adjoint Banach algebra 88
Banach algebra, semi-simple Banach algebra 76
Banach space 13
Banach space, reflexive Banach space 20
Basis 3
Bessel's inequality 26
Bochner theorem 97 142
Boundary 80
Carrier 84
Cartesian product 10
Central element (function) 105 157 175
Character group 137
Character, generalized 180
Character, of a compact group 159
Character, of an Abelian group 135
Character, of an algebra 71
Character, real 132
Closed graph theorem 17 18
Closed set (closure) 4
Compact set 5
Compactification, of a completely regular space 55 56
Compactification, one-point 7
Completely regular space 55
Complex -space 46
Conjugate space 18
Continuity 4
Convolution 120-122
Daniell integral 29 (
Direct integral 176
Direct sum 16
Directed set 1 2
Ditkin, condition of 86
Dual algebra 161
Equivalent functions 36 37
Extendable linear functional 96
Factor 176
Finite intersection property 5
Fourier series 153 (
Fourier transform 71 135
Fubini theorem 44
Function algebra 53
Function algebra, inverse closed 54
Function algebra, regular 57
Function algebra, self-adjoint 55
Gelfand representation 53 70
Group algebra (ring) 123 31
H lder inequality 37 46
Haar integral 115 29
Haar integral, normalized 144 154
Haar integral, on quotient spaces 130 33
Hahn - Banach theorem 19 20
Hausdorff space 5
Heine - Borel property 4
Herglotz - Bochner - Weil - Raikov theorem 97 142
Hilbert space 23 24 (
Homeomorphism 4
Hull 56
Hull-kernel topology 56 60
Idempotent 101
Idempotent, reducible idempotent 101
Identity, added to an algebra 59
Identity, modulo an ideal 58
Integrable function (and set) 34
integral 30
Integral, bounded 34
Integral, on Cartesian products 44
Integral, the Haar integral 115 29
Interior 4
Invariant subspace 125
Inversion theorem 143
Involution 28 87
Irreducible idempotent 102
Irreducible representation 163
Kernel 56
Laplace transform 74 179
Linear functional, bounded 18
Linear functional, extendable 96
| Linear functional, positive 96
Linear functional, unitary 99
Linear order 2
Linear transformation, bounded 15
Linear transformation, self-adjoint 95
Linear transformation, unitary 127-129
Local membership in an ideal 85
Locally compact space 7
Maximal ideal space 54 69 23
Mean value of von Neumann 169
Measurable set (and function) 36
Measure 34
Measure, on a Cartesian product 45
Minimal left ideal 102
Minimal two-sided ideal 102
Minkowski inequality 38 46
Modular function 117 132
Monotone family of functions 32
Monotone family of functions, -monotone family 33
Neighborhood 4
Neighborhood, symmetric neighborhood 108
Norm 13
Norm, -norm 37 46
Norm, Banach algebra norm 16 48
Norm, of a bounded transformation 15
Norm, uniform norm 9 14 39
Normal space 6
Normed algebra 16
Normed field 68
Normed linear space 13
Null function 35
Null set 35
Null space 16
One point compactification 7
Open set 3
Orthogonal complement 25
Parallelogram law 23
Parseval's equation 155 175
Partial order 1
Plancherel theorem 99 145 174
Poisson summation formula 152
Pontriagln duality theorem 140 151
Positive definite element 98
Positive definite function 126 142
Positive linear functional 96
Primary ideal 181
Projection, in Hilbert space 25 26
Projection, onto a coordinate space 11
Pseudo-norm 52
Quotient space 14 110
Radical 76
Radon - Nikodym theorem 41
Real character 132
Reduction theory 175
Reflexive Banach space 20
Regular Banach algebra 82 (
Regular function algebra 57
Regular ideal 58
Relative topology 4
Representation, irreducible 163
Representation, of a group 127
Representation, of an algebra 163
Representation, of an algebra 92
Representation, regular 130
Scalar product 24
Schwarz inequality 24
Self-adjoint element 90
Semi-direct product 119
Semi-simple ring (algebra) 62 76
Silov's theorem 151
Spectral norm 75
Spectral theorem 94 95
Spectrum 64
Stone - Weierstrass theorem 9
Stone's theorem 147
Sturm - Liouville differential equations 182
Sub-basis 3
Summable function 31 33
Summable set 34
Symmetric neighborhood 108
Tauberian theorem 85 148 180
Topological group 108
topology 3
Topology, 111
Topology, compact 5
Topology, completely regular 55
Topology, Hausdorff 5
Topology, hull-kernel 56 60
Topology, locally compact 7
Topology, normal 6
Topology, relative 4
Topology, weak 10
Triangle inequality 13 24
Tychonoff theorem 11
Uniform norm 14
Unimodular group 117
Unitary functional 99
Urysohn's lemma 6
Variations of a functional 40
Weak topology 10
Weak topology, on a conjugate space 22
Weight function 74 180
Wiener Tauberian theorem 85 148 180
Zorn's Lemma 2
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