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Szkelyhidi L. — Discrete Spectral Synthesis and Its Applications

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Название: Discrete Spectral Synthesis and Its Applications

Автор: Szkelyhidi L.

Аннотация:

In order to study discrete Abelian groups with wide range applications, the use of classical functional equations, difference and differential equations, polynomial ideals, digital filtering and polynomial hypergroups is required. This book covers several different problems in this field and is unique in being the only comprehensive coverage of this topic. It should appeal to graduate students and researchers in harmonic analysis, spectral analysis, functional equations and hypergroups.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 120

Добавлена в каталог: 27.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

-norm      8
0-dimensional      41
Abelian group      ix—xiv 8—11 14 16 17 19 21—23 25 34—37 49—52 57—62 69 77 94
Absolutely convergent      3
Additive      iv v xiii xiv 19 22 26 34 36 37 44 98 105
Additive function      x 19 20 22 25 26 35 36
Adverse      3
Algebra      4
Algebra homomorphism      1 2 4 9
Algebra with involution      92
Algebraic dual      2
Almost everywhere      9
Annihilator      11 18 20 23 26 28 30 31 38 49 50 69 93 97 107 108
Annihilator ideal      22 23 29 38 86 94
antisymmetric      67
Approximate identity      12 13
Approximation theorem      10
Baire measure      10
Banach algebra      3 4 7
Banach space      3 4 12
Banach — Alaoglu theorem      4
Beurling problem      15 16 41
Bi-additive      34—37 44 61 67
Bijective      2—4
Bilinear      44 91
Bochner's theorem      9
Boundary      17
Canonical representation      78
CHARACTER      9 14 18 26 38 61
Characteristic differential equation      87
Characteristic differential equation system      87 89 90
Characteristic polynomial      18 19 85 87 88
Characteristic root      18
Closed      ix—xi 3 4 7 8 11—15 17—21 23 26 36 45 49 57 65 71 86
Closed ideal      4 7 8 10—16 19 20 28 93 97
Closed linear subspace      ix 72 77 93
Closed proper ideal      20
Closed subgroup      50
Closed subspace      10—12 20 88 93
Closed translation invariant subspace      93
Closed under differentiation      32 33
Closure      4 10 15 101
Co-cycle equation      66 67
Co-final      40
Commutative      2 7 91 92
Commutative algebra      2 7 17 93
Commutative Banach algebra      3 4 7 8
Commutative hypergroup      91—94 96
Commutative normed algebra      3
Commutative semigroup      27 28
Commutative topological group      x
Compact      ix x 4 7—11 16 17 19 26 27 40 50 69 71 76 92
Compact Haussdorff space      4
Compact support      7
Compactly generated      50 51
Compactly supported      17 19 20 50 69 71 91
Complete regularity      4
COMPLEX      17—19 52 65 79 80 86 96—98
Complex additive function      44
Complex algebra      1
Complex algebra homomorphism      1
Complex field      3
Complex function      x 4 17
Complex measure      17 26 51 91 97
Complex number      ix x 1 15 17 19 26 28 31 62 63 65 66 87—90 96 98—101 103—106
Complex polynomial      19 20 22 28 29 56 79 80 84 97 101
Complex Radon measure      19 50 69
Complex unit root      63
Complex valued      59 61
Complex variable      28 29 103
Complex-valued      ix x 2 4 9 17 19 29 34 35 69 70 92 93 95 97
continuous      iv vii 4 8 9 12 14 21 71 73 74 76 91—93
Continuous function, ix, x      1 4 9 17 19 71 92 93
Continuous homomorphism      19
Continuous mapping      91
Continuous multiplicative linear functional      3
Convergent      3 66 75 76
Convex      10
Convex combination      9
Convex hull      52
Convex set      10
Convolution      xi xiv 8 17 19 30 49 69 73 77 91—94 97 103
Convolution formula      95 97
Convolution of measures      17
Convolution type functional equation      50 51 69 77
Covariant      73
Covariant mean      77 78
Cube equation      52
Cyclic group      26
D'Alembert equation      13
d-dimensional polynomial hypergroup      103—105
Deblurring      60
Degree      43
Dense      ix x 7 8 10 15 17—20 22 23 28 31 36 50 65 74 84 100 107 108
Dense subspace      40
Denumerable      vi 17
Diagonalization      43
Difference equation      x xi xiv 18 21 69 70 76 83—90
Differential      vii 84 89
Differential equation      ix xiv 23 33 34 57 64 79 80 86 87 89 90
Differential operator      28 34 52 53 56 57 59 80 84 86 88 107
Differential polynomial      31
Digital image      60 61
Dirac measure      18
Direct complement      39
Direct product      15
Direct sum      37
Discrete      x xi xiii xiv 8 9 16 17 21—23 26 51 71 96 103
distribution      23
Distribution theory      10
Divisible      25 26 45 61
DJS hypergroup      91
Dual      2—4 8 9 11 12 16 17 19 26 29 41 63 91 93
Dual object      1
Duality      1 9
Duality Theorem of Pontryagin      9
Duality theory      41
Ehrenpreis — Palamodov theorem      34
enhancing      60
Even      53 55 57
Exponential function      ix x 25 28 65 66 71 77 96 104
Exponential monomial      ix x 18—23 25 26 28 30 31 35 36 49—51 57—59 65 66 70—75 84—87 94 98 100 107 108
Exponential polynomial      xiv 20 28 45 66 70 73 75—81 84 98 107 108
Exponential, be      18—22 28 29 35 45 49 50 52 57 65 70—80 84 85 90 94—98 104 105 107
Extension      38 40
Faithful      1
Fejer's theorem      12
Field      3 38
Field isomorphism      38
Filter      60—62
Filtered image      61
Filtering      xi xiv 60
Finite abelian group      40
Finite dimension      45
Finite group algebra      38
Finite intersection property      27
Finite order      25
Finitely generated      xi xiv 21 23 26 33 51 57—60
Finitely generated subgroup      40
Finitely supported measure      41
Fourier series      76
Fourier transform      9—11 14—16 19 20 41 63 71 74 76—78 80
Fourier transformation      9 10 61 63 74 75 79 80
Fourier-Laplace transform      20 28—30 71 94 97 98 101 107 108
Fourier-Laplace transformation      29
Frechet's equation      42
Free Abelian group      27
Function algebra      1 2 4
Gelfand transform      xii 2
Gelfand transformation      1—3

Gelfand — Mazur theorem      3
Generalized character      18 19
Generalized character group      19
Generalized dual      19
Generalized monomial      43
Generalized polynomial      43
Haar measure      10
Hahn — Banach theorem      1 12 39 93
Hamel basis      37
Haussdorff group      92
Haussdorff space      4 5 7 8 16 91 92
Height      53 56
Hermitian      92
Hermitian hypergroup      92 95
Homeomorphism      4 91
Homogeneous term      43
Homomorphic image      21
Homomorphism      x 1 2 21 25 26 43 58 60
Homomorphism theorem      2
Ideal      xiii 2 4 7 12 13 16 18 19 29—34 49 50 56 57 69 86 93 97 98 101 107 108
Identity      3 4 7 8 12 13 17 56 71 73 79 83 88 91 92 96 104 115
Image      60—62
Infinite order      27
Infinitely differentiable      21 23
Injective      2
Intermediate ideal      2
Inverse      3 10 12 92
Inversion theorem      10 15
Isometrically isomorphic      3
Isomorphic      2 25 26 37
Kernel      2 3 8 13 17 84 93
Lasker — Noether Theorem      29
Leading term      43
Left translation operator      92
linear combination      x
Linear functional      1 2 9 29 39 93
Linear hull      ix x 21 23 31 36 50 55 65 100 101 107 108
Linear space      ix x 1 2 32 33 35 37 65 86 88
Linearization coefficients      95
Linearization formula      95 96 101 103—105
Linearly independent      45
Locally compact      ix x xiii 4 5 8—11 14 16 17 19 22 23 28 49 50 69 77 91—94
Locally compact Abelian group      16
Locally compact group      16
Locally convex      19 45 69 70 77 92 93
Malliavin's Theorem      16
Maximal cardinality      27
Maximal element      7
Maximal ideal      2—4 7—9 11 13—17 19 34 38
Maximal ideal space      3 8 9 17 18
Maximal independent system      27
Mean periodic      xiv 20 69—78
Mean value operator      73
Mercer's theorem      9
Michael topology      92
Monomial equation      43
Moore — Smith convergence      75
Multi-index      28 32 33 53—59 79
Multiplication      8
Multiplicative group      45
Multiplicative linear functional      1 2 8 13 17 18
Multiplicity      18 33
Multiplicity spaces      34
Multivariate hypergroup      103
Multivariate polynomial hypergroup      105 107 108
n-additive      43
n-th root of unity      38
Natural homomorphism      3 38
Net      13 40 66
Net-convergence      13
Newton interpolation formula      22 32
Noetherian operator      34
Non-complete direct product      45
Norm-decreasing      4 9
Norm-preserving      10
Normal exponential polynomial      45
Normalization      105
Normalizing point      105
Normed algebra      3
Normed field      3
Nullstellensatz      29 31 41 98 107
Octahedron equation      52
Odd part      62
Orthogonal polynomial      95
Partial differential equation      xiv 23 33 57 64 79 80 86 87 89 90
Partial differential operator      23 80 86
Partial translation operators      83
Partially ordered set      7 13
Perfect set      17
Periodic      71 76
Permutation      43
Plancherel's Theorem      10
Pointwise convergence      40
Polynomial      x 19 21 22 29—36 52—60 63—66 70—74 76—78 80 81 84—86 88—90 95—98 100 101 103—108
Polynomial equation      42
Polynomial functions      42
Polynomial hypergroup      xi xv 96—98 100 101 103 105 107
Polynomial ideal      xiii 29 52 107
Polynomial ring      29 31 34 86
Polynomial-valued      74
Positive definite      9
Positive measure      9
Primary ideal      16 19 20 29 34
Primary Ideal Theorem      16 41
Prime ideal      34
Primitive root of unity      63
Principal ideal      22 23 31 101
Product group      45
Projection      45
Radical      3
Radical ideal      34
Radon measure      17 20
Rank      27
Regular      2 4
Regular Banach algebra      7
Regular ideal      2—4 7 8 11 14
Regular measure      91
Regularity      2
Relative identity      2
Restriction      8 39
Riemann — Lebesgue lemma      9
Right translation operator      92
Scalar product      10
Semi-simple      3
Semigroup      27
Separating family      2
Series      3
Sharpening      60
Simple root      18
Smoothing      60
Space of mean periodic functions      69
Spatial filtering      60
Spectral analysis      ix—xiii xv 7 10 11 13—15 18 21—23 26—28 31 91 94 107
Spectral set      xiv 42 49—51 85—90
Spectral synthesis      ix—xv 8 13—16 19 21—23 26—29 35 50—52 57 59 61 65—67 71—73 75—77 83 84 91 94 98 100 107 108
Spectrum      14—17 49 50 84 85
Stone Weierstrass Theorem      8
Structure theory      16
Sub-net      40
Sup-norm      4
Support      15 26 50 51 78 92
Surjective      1
symmetric      34 35 37 43 66
System of characteristic equations      85
System of convolution type equations      50
System of convolution type functional equations      52
Tauberian theorem      10 11 26
Taylor formula      22 32 45 56 84 86
Topological space      40
Topological vector space      19

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