Akhiezer N.I. — The classical moment problem and some related questions in analysis :: Электронная библиотека попечительского совета мехмата МГУ

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Akhiezer N.I. — The classical moment problem and some related questions in analysis

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Название: The classical moment problem and some related questions in analysis

Автор: Akhiezer N.I.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1965

Количество страниц: 253

Добавлена в каталог: 04.11.2012

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Предметный указатель

-th abbreviated matrix      28
$\mathcal{F}$ -matrix      2
$\mathcal{F}$ -matrix, bounded      7
Akhiezer      50 87 89 124 126 131 185
Analogue of Green’s formula      9
Analogue of Green’s formula, the Christoffel — Darboux equation      184
Analogue of Green’s formula, the Liouville — Ostrogradskii formula      9
Analogue of Green’s formula, Weyl’s finite difference theorem      15
Artemenko      192
Banach’s criterion      42
Bernstein      203 204 206 210
Bessel’s inequality      38
Bochner      192
Caratheodory      90 91
Carleman      vii 24 85
chebyshev      v vi 24 64 113
Christoffel — Darboux formula      9
Class C      91 94
Class N      92 94
Class of pseudo-positive functions      94
Class R      94
Class R(E ${}_{\infty}$ )      200
Cramer      226 227
Criterion, Hamburger’s      84
Criterion, of completeness      42
Defect, Parseval’s      122
Dennis      25
Finite vector      35
Fourier coefficients, generalized      38
Fourier series, generalized      38
Fraction, continued      23
Fraction, continued associated      113
Fraction, continued Stieltjes      232
Function, absolutely monotonic      203
Function, absolutely monotonic, of several variables      228
Function, exponentially convex      210
Function, exponentially convex, of many variables      229
Function, hermitian positive      190 192
Function, hermitian positive, radial      198
Function, of class $K_{\alpha}$       218
Function, of class $P(E_{m})$       194
Function, of class $P_{\alpha}$       191
Function, of class $P_{\infty}$       215
Function, of class $W_{a, b}$       210
Function, of class $\mathfrak{M} (a, b)$       203
Function, of class $\mathfrak{U}$       161
Function, of class T      208
Function, of minimal exponential type $\rho(z)$       49 56 60
Function, of minimal exponential type $\rho_{n}(x)$       62
Function, of minimal exponential type $\rho_{n}(z)$       49 60
Functional, directing      159
Functional, positive      2 60 153
Functional, positive integral representation for      153
Functional, positive integral representation for $\mathfrak{S}$       2
Functional, positive integral representation for, $\mathfrak{C}$       181
Functional, positive integral representation for, $\mathfrak{K}$ -positive      69
Gel’fand      47
Generating element      147
Geronimus      104 188
Glazman      131
Gnedenko      213
Gurarii      89
Hamburger      vii 11 84 88 146 172
Hardy      87
Hausdorff      203
Hellinger      vii 11 16
Herglotz      91
Hildebrandt      76 228
Interval of continuity      194
Jacobi matrix      2
Kats      129
Kernel polynomial of degree       9
Khinchin      192 217
Kilpi      174
Kolmogorov      185
Koranyi      174
Krein      87 104 126 127 129 131 132 133 153 172 185 186 192 213 215 217 219 232 234 236
Levin      173
Levy (P.)      217
Livshits      153 156 192
M. Riesz      68
Markov      v vi 24 64 113
Mathias      192
Matrix, Nevanlinna      8 55
Matrix, of type       19
Matrix, of type       19
Matsaev      132
Measure      194
Method of directing functionals      153 159
Moment, generalized, of order       v
Nagy      174
Naiman      131
Nevanlinna      vii 11 16 90 92 101 104
Nevanlinna’s formula      92
Normal property of an operator      174
Numerator, corresponding to a quasiorthogonal polynomial      11
Operator,       35 36 185
Operator, adjoint      139
Operator, hypermaximal      174
Operator, isometric      36
Operator, normal      174

Operator, symmetric      139 146
Operator, symmetric, simple      152
Operator, unitary      39
Ostrovskii      132
Parseval’s equality      38
Perron      124
Pick      104
Polya      86
Polynomial,       65
Polynomial, $R^{*}(z)$       183
Polynomial,       66
Polynomial, Bernstein’s      75
Polynomial, of first and second kinds      8
Polynomial, orthogonal on a circle      182
Polynomial, orthonormal relative to a sequence      3
Polynomial, quasi-orthogonal of degree n      10
Polynomials related to Jacobi matrices      8
Prawitz      80
Problem of moments      v vi
Problem of moments, associated with the operator       141
Problem of moments, classical      70
Problem of moments, complex      174
Problem of moments, determinate      vi. 29
Problem of moments, extended      vi
Problem of moments, general      154
Problem of moments, Hamburger’s      29 240 241
Problem of moments, Hausdorff’s      73
Problem of moments, Hausdorff’s, solubility criterion      74
Problem of moments, Hausdorff’s, two-dimensional      228
Problem of moments, indeterminate      29
Problem of moments, indeterminate, canonical solution      113
Problem of moments, Livshits’ generalized      154
Problem of moments, of Nevanlinna — Pick in the Class N      104 109
Problem of moments, of Schur’s coefficients      101
Problem of moments, on limiting values of integrals      vi
Problem of moments, power      29 95
Problem of moments, power, solubility criterion      29
Problem of moments, Stieltjes      240
Problem of moments, Stieltjes’, full      76
Problem of moments, Stieltjes’, indeterminate      88
Problem of moments, trigonometric      178
Problem of moments, trigonometric, solubility criterion      180
Problem of moments, truncated      30
Problem, in theory of analytic functions      90
Problem, interpolation, condition of solubility      121
Problem, interpolation, of Nevanlinna, Pick      174
Problem, of Carath $\acute{e}$ odory coefficients      178
Quadrature formulae      21 49
Quasi-polynomial      181
Rekhtman      104
Resolution of unity      142
Resolution of unity, orthogonal      142
Riesz, F.      68 91
Riesz, M.      vii 11 68 71 78
Schoenberg      76 203 207 208 228
schur      90 92 101
Schur, parameters      103
Sequence, canonical, of nodes      165
Sequence, non-negative with respect to circle      180
Sequence, non-negative with respect to interval      70
Sequence, of masses      165
Sequence, of polynomials      14 54
Sequence, positive      1 2
Shvetsov      297
Sierpinski      210
Solution, -extremal      45 114
Solution, -extremal      46
Solution, canonical, of order       115
Solution, extremal at a point      43
Sonin      201
Spectral function      142
Spectral function, orthogonal      142
Spectrum, simple      146
Stieltjes      v vii 64 67 88 126
Stieltjes — Perron inversion formula      124
Szeg $\ddot{o}$       182 188 201
Theorem, analyticity      19
Theorem, Berezanskii’s      26
Theorem, Bochner’s      195
Theorem, Carath $\acute{e}$ odory — Toeplitz      178
Theorem, Hausdorff’s      74
Theorem, Hellinger’s      11
Theorem, Invariance      16
Theorem, Naimark’s      47
Theorem, on extension of a positive functional      69
Theorem, on zeros      184
Theorem, Riesz (F.) — Herglotz      180
Theorem, Stieltjes      237
Theorem, Stone’s      149
Theorems, Bernstein’s      204 210
Theorems, Hamburger’s      30 95 240
Theorems, Krein’s      127 160 219
Theorems, Livshits      156 158
Theorems, Nevanlinna’s      95 98
Theorems, Riesz’ (M.)      43
Theorems, Schoenberg’s      198 200 208
Theorems, Widder’s      207 210
wall      25
Weyl      11 15 16
Widder      203 210
Wold      226 227
Wouk      25 26

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