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.

Аннотация:

This book explains the classical moments problem, which can be applied to reconstruct distribution functions, electrical conductivities tensors…in plasmas, partially ionized gases, etc.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1965

Количество страниц: 253

Добавлена в каталог: 28.03.2010

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

Предметный указатель

$\mathscr{J}$ -matrix      2
$\mathscr{J}$ -matrix bounded      7
Akhiezer      50 87 89 124 126 131 185
Analogue of Green's formula      9
Analogue of the Christoffel — Darboux equation      184
Analogue of the Liouville — Ostrogradskii formula      9
Analogue of 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 $R(E_{\infty})$       200
Class C      91 94
Class N      92 94
Class of pseudo-positive functions      94
Class R      94
Cramer      226 227
Criterion of completeness      42
Criterion, Hamburger's      84
Defect, Parseval's      122
Dennis      25
Finite vector      35
Fourier coefficients, generalized      38
Fourier coefficients, series, generalized      38
Fraction, continued      23
Fraction, continued associated      113
Fraction, continued Stieltjes'      232
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
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
Functional, directing      159
Functional, positive      2 60 153
Functional, positive integral representation for      153
Functional, positive integral representation for $\mathcal{K}$ -positive      69
Functional, positive integral representation for $\mathcal{S}$       2
Functional, positive integral representation for $\mathfrak{C}$       181
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 n      9
Khinchin      192 217
Kilpi      174
Kolmogorov      185
Koranyi      174
Krein      87 104 126 127 129 131—133 153 172 185 186 192 213 215 217 219 232 234 236
Levin      173
Levy (P.)      217
Livshits      153 156 192
Markov      v vi 24 64 113
Mathias      192
Matrix of type C      19
Matrix of type D      19
Matrix, Nevanlinna      8 55
Matsaev      132
Measure      194
Method of directing functionals      153 159
Method of Riesz', M.      68
Moment, generalized, of order k      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 U      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
p-th abbreviated matrix      28
Parseval's equality      38
Perron      124
Pick      104
Polya      86
Polynomial of first and second kinds      8
Polynomial R(u)      65
Polynomial R*(z)      183
Polynomial S(u)      66
Polynomial, Bernstein's      75
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 in theory of analytic functions      90
Problem of Caratheodory coefficients      178
Problem of moments      v vi
Problem of moments associated with the operator A      141
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, 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, 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, interpolation, condition of solubility      121
Problem, interpolation, of Nevanlinna, Pick      174
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 of masses      165
Sequence of polynomials      14 54
Sequence, canonical, of nodes      165
Sequence, non-negative with respect to circle      180
Sequence, non-negative with respect to interval      70
Sequence, positive      1 2
Shvetsov      297
Sierpinski      210
Solution extremal at a point      43
Solution, canonical, of order m      115
Solution, N-extremal      45 114
Solution, V-extremal      46
Sonin      201
Spectral function      142
Spectral function, orthogonal      142
Spectrum, simple      146
Stieltjes      v vii 64 67 88 126
Stieltjes — Perron inversion formula      124
Szegoe      182 188 201
Theorem on extension of a positive functional      69
Theorem on zeros      184
Theorem, analyticity      19
Theorem, Berezanskii's      26
Theorem, Bochner's      195
Theorem, Caratheodory — Toeplitz      178
Theorem, Hausdorff's      74
Theorem, Hellinger's      11
Theorem, Invariance      16
Theorem, Naimark's      47
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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