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Shohat J. — The problem of moments
Shohat J. — The problem of moments

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Название: The problem of moments

Автор: Shohat J.

Аннотация:

The problem of moments is of fairly old origin, but it received its first systematic treatment in the works of Tchebycheff, Markoff, Stieltjes, and, later, Hamburger, Nevanlinna, M. Riesz, Hausdorff, Carleman, and Stone. The subject has an extensive literature, but has not been treated in book or monograph form. In view of the considerable mathematical (and also practical) interest of the moment problem it appeared to the authors desirable to submit such a treatment to a wide mathematical public. In the present monograph the main attention is given to the classical moment problem, and, with the exception of a few remarks concerning the trigonometrical moment problem, no mention is made of various generalizations and modifications, important as they may be. Furthermore, lack of space did not permit the treatment of important developments of Carleman and Stone based on the theory of singular integral equations and operators in Hilbert space. On the other hand, a special chapter is devoted to the theory of approximate (mechanical) quadratures, which is intimately related to the theory of moments and in many instances throws additional light on the situation.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1970

Количество страниц: 144

Добавлена в каталог: 06.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
${\mathfrak{G}}_{0}$ Moment-Problem      1 10 11 13
Abel      ix 131
Absolute moments      14 137
Achyeser and Krein      xi 5 7 76 82 85 86 127
Additive functions      xi xii
Approximate (mechanical) quadrature      ix 37 41 79 106
Associated continued fraction      vii 33 51 73 107 108 117 138
Asymptotic series      xi 27 32
Banach      100 127
Bernstein's polynomial      8 9 99 101
Bernstein, S.      8 9 90 99 101 127 137
Boas      103 104 105 128
Bochner      xii xiii 128
Borel      104 127
Carleman, T.      x xi 19 123
Closure property      x see
Completely monotonic functions      86 87 89 90
Completely monotonic sequences      86 88 101 104 105 138
Corresponding continued fraction      vii 74 107 117 121
Cramer      xi 21 128
Determined Moment-Problem      viii x 5 6 7 9 10 11 13 20 21 45 50 51 56 57 59 66 68 69 70 75 96 122
Distribution function of order $\geqslant n$      42 44 45
Distribution function, distribution set function      vii xi 1 2 4 21 75 87 88 89 93 108 126 130 133 137
Erdos and Turan      125
Extremal properties      x 60 75 117
Fejer      114 129
Fischer      5 85 129
Frechet, M.      82 129
Generalized approximants      33 47 51 53
Hallenbach      105 130
Hamburger Moment-Problem      4 5 11 13 19 21 23 33 66 72 75 76 103 107 113 123
Hamburger, H.      x 4 5 11 13 19 20 21 23 33 50 61 66 69 70 72 75 76 103 107 108 113 117 123 127 130 132 135
Hankel quadratic form      4
Hardy      20 96 97 130
Hausdorff      x xi 8 78 86 87 90 93 08 102 104 105 120 129 130 131
Hausdorff one-dimcnsional moment-problem      8 9 86
Hausdorff two-dimensional moment-problem      9
Haviland      x xiv 19 21 130 131
Hedge      21 131
Heine      ix
Helly      x xii xiii 12 45 68
Helly's Theorems      x xiii 12 45 68
Herglotz      24
Hermitc      ix 118 131 132 136
Hermitc polynomials      122 129
Hildebrandt and Schqcnbcrg      8 105 131
Hille      93 131 138
Indeterminate Moment-Problem      viii x 22 50 51 52 59 60 65 68 69 75 76 105
Interpolation      ix
Jackson      125 131
jacobi      9
Jacobi polynomials      92
Jouravsky      112 119 122 123 131
Kaczmarz und Steinhaus      102 131
Kantorovich      xiv 131
Krawtchouk      126 132
Laguerre      ix 92 93 122 128 129 132
Laguerre polynomials      92 93 122
Laplace      ix 89 90 93 94 129 131 138
Laplace Stieltjes integral      89 90 93 94 138
Le Roy      96 132
legendre      ix 90 124
Legendre polynomials      90 124
Markoff, A.      x 43 76 80 82 114 118 127 133 134 136
Mechanical quadratures      129 131 133 135 136 137 138 see
Moment functions      86 87 88 89 92
Moment sequences      86 87 92
Netzorg      125 133
Nevanlinna, It.      x xi 61 66 133
Non-negative functional      xii 1 2 3 10 105 121
Non-negative functional, extension of      xii 2 10 121
Normal distribution      ix
Ortho-normal polynomials      35 40 47 51 61 67 78
Orthogonal polynomials      ix x 35 36 39 130 132 133 136 137 138
Ostrowski      14 134
Parscval Formula (closure property)      x 61 62 66 75 134 136
Perron      20 47 73 74 134
Point spectrum      xi
Polya      104 134 136 138
Polya und Szego      4 7 8 16 76 134
Positive (non-negative) sequences      78
POSSE      76 79 80 134
Quadratic forms properly, improperly definite      71 75
Quadrature abscissas      106 111 113 114 115 116 125
Quadrature coefficients      39 41 106 108 109 116 117 125
Quadrature coefficients, extremal property of      39 125
Quasi-orthogonal polynomials      x 35 36 37 39 41 45 48 66 67 73 75 78 79 107
Reduced moment-problem      28 34 35 37 39 76 115
Riesz, M.      x xi 20 35 61 66 69 70 110 111 134
Schocnbcrg      90 135
Shohat      108 111 112 129 135
Spectrum      xi 5 6 7 11 33 42 43 44 51 73 78 79 111 132
Stieltjes      vii viii xiv 5 6 11 19 20 22 41 43 66 72 73 74 75 76 94 96 103 107 108 109 113 114 117 121 122 123 127 128 129 130 131 135 136 137 138
Stieltjes, Inversion Formula      xiv 29 57 97
Stieltjes, Moment-Problem      5 6 11 19 20 66 72 73 74 75 76 96 103 107 108 109 113 114 121 122 123
Stieltjes, Moment-Problem, modification of      104 105
Stieltjes, Vitali Theorem      viii 14 33 74 121
Stone      xi xiv 59 60 136
Stridsberg      20 136
Substantial convergence      xii 110
Substantial equality      xi 2 9 11 27 65 88 98
Szegoe      125 136
Tamarkin      90 131 137
Tchebycheff      ix x 43 77 82 115 125 126 133 135 136 137
Tchebycheff, Inequalities      10 43 82 115 125 133 135
Titchmarsh      53 57 96 137
Toeplitz form      7 127
Trigonometric Moment-Problem      xi 6 128 132
True interval of orthogonality      113
Uspensky, J. V.      76 119 122 137 138
Verblunsky, S.      xi 82 127 137
Vitali theorem      viii 14 33 121
Wald, A.      82 137
Widder, D. V.      90 92 93 94 95 96 137 138
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