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Loomis L.H. — An introduction to abstract harmonic analysis
Loomis L.H. — An introduction to abstract harmonic analysis

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Название: An introduction to abstract harmonic analysis

Автор: Loomis L.H.

Аннотация:

Harmonic analysis is a branch of advanced mathematics with applications in such diverse areas as signal processing, medical imaging, and quantum mechanics. This classic monograph is the work of a prominent contributor to the field. Geared toward advanced undergraduates and graduate students, it focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1953

Количество страниц: 198

Добавлена в каталог: 25.11.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^{*}$ algebra      28
$C^{*}$ algebra, commutative $C^{*}$ algebra      88 91
$H^{*}$ algebra      100 27
$L$-bounded function      33
$L$-monotone family      33
$l^{p}$-norm      37 46
$L^{p}$-space      37 14
$L^{p}$-space, complex $L^{p}$-space      46
$T_{1}$-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, $C^{*}$ algebra      28 88 91
Banach algebra, $H^{*}$ 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 $L^{p}$-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$\ddot{o}$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, $L$-monotone family      33
Neighborhood      4
Neighborhood, symmetric neighborhood      108
Norm      13
Norm, $L^{p}$-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 $H^{*}$ 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, $T_{1}$      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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