Peyerimhoff A. — Lectures On Summability :: Электронная библиотека попечительского совета мехмата МГУ

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Peyerimhoff A. — Lectures On Summability

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Название: Lectures On Summability

Автор: Peyerimhoff A.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1969

Количество страниц: 111

Добавлена в каталог: 10.09.2008

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Предметный указатель

$C_{\alpha_{\nu}}$ $(C_{O})$       11
$M_{p}$       16—17 25—27 31 37 44 46 55—57 60—61 63
$RS_{\alpha}$       11
(A, $\lambda$ ) method      69
A* method      88—89
Abel      3
Abel — Dini theorem      12
Abel's limit theorem      24 67
Abel's method      24—26 62 67 70—71 75—77 84
Abelian theorems      67
Agnew      92
Analytic continuation by Borel's method      72 76
Analytic continuation by Euler's method      73 95—96
Analytic continuation by Hausdorff methods      93—96
Analytic continuation, general      71—73
Arithmetical means      see " $M_{p}$ "
Axer's theorem      87
Banach      30 95
Basu      50
Bernstein      53
Bohr      42
Bohr — Hardy theorem      43 45
Borel's method      24—26 62 68 72 75—78 81—82
Borel-star      76
Bosanquet      42 43
Cesaro      2
Cesaro methods, $C_{1}$       3—8 16 25—26 31 36 38 46 55 59 66 74—75 80—81
Cesaro methods, $C_{\alpha}$       8—9 15—17 22 24—25 27 33 35 38 42—43 45 47—48 50 55 66 76 82 96 99—100
Cesaro's theorem      2
Chow      7
Comparison theorems, $C_{\alpha}$ , $C_{\beta}$       15 38 66
Comparison theorems, $C_{\alpha}$ , $E_{p}$       25 77 79
Comparison theorems, $C_{\alpha}$ , $H^{\alpha}$       8 29 47—48 50
Comparison theorems, $C_{\alpha}$ , Abel      25 76 81
Comparison theorems, $C_{\alpha}$ , Borel      76
Comparison theorems, $E_{p}$ , Borel      25
Comparison theorems, $M_{p}$ , $M_{q}$       37
Comparison theorems, $N_{p}$ , $C_{1}$       38
Comparison theorems, $N_{p}$ , $N_{q}$       37—38
Comparison theorems, A*, Hausdorff      89
Comparison theorems, Abel, Borel      76—77 79
Comparison theorems, general      15—16 26 29 36—37 56 98—99
Comparison theorems, Hausdorff, $E_{p}$       25
Comparison theorems, Lambert, Abel      84
Comparison theorems, Riesz      24—26 37 99—100
Completely monotone function      53
Consistency, first theorem of      25
Consistency, second theorem of      37
Consistent      18
Consistent methods      18—19 22 29—30 88 91—92
Convergence factors      39
Convergence generating      13
Convergence preserving      12
Convexity theorem      63—64
Counting function      57
De La Vallee Poussin      84 88
Dedekind      38
Dirichlet series      24
Divided differences      51
du Bois-Reymond      38
Equivalent      15
Euler means $E_{p}$       20 22 25 29 31—32 46 60 62 67—68 72—74 95—96
Exact region of summability      76 92—96
Fejer      4
Frobenius      25
Function of a matrix      51
Gaier      75
Gap-series      73
Gap-Tauberian theorem      74—76
hadamard      84 88
Hadamard's gap theorem      75
Hardy      7 18 42 80
Hardy — Littlewood      75 76 82
Hausdorff      47
Hausdorff means      20—25 28 47 49 88—96
Hausdorff means, order of      25
Hausdorff moment problem      23
High indices theorem      17
Hill      29
Hoelder's method, $H^{2}$       10
Hoelder's method, $H^{k}$       8—9 22 29 47—50 56
inclusion      see "Comparison theorems"
Jurkat      24 70
Karamata      70
Knopp      20 25 47 50
Knopp — Lorentz theorem      13
Knopp — Schnee — (Hausdorff) theorem      8 29 48
Knopp — Schnee — (Hausdorff) theorem, generalized      56

Kuttner      24
Lambert's method      82—84
Landau      7
Limitable      3 15
Littlewood      67 70
Lorentz      57 73
Matrix method      16
Mazur      26 29
Mazur — Orlicz theorem      29
Mean value conditions, $C_{\aplha}$       31 33 35
Mean value conditions, $E_{p}$       32
Mean value conditions, $H^{\aplha}$       48—49
Mean value conditions, $M^{*}_{K}(A)$       34
Mean value conditions, $M_{K}(A)$       31
Mean value conditions, $M_{p}$       31
Mean value conditions, $N_{p}$       35
Mean value conditions, general      31—36 53
Mercerian theorem      50
Mittag-Leffler star      73
Moebius functions      85
Moment function      28
Moment sequence      23 25 89
Muentz approximation theorem      95
Noerlund mean $N_{p}$       17—19 25 28 30 35 37—38 45—46 61 88 91—92 96—99
Noerlund mean $N_{p}$ , generalized      97
normal      14
Okada      73
One-sided      7
Order conditions for limitable sequences, $C_{1}$       4
Order conditions for limitable sequences, $C_{\alpha}$       15
Order conditions for limitable sequences, $E_{p}$       22
Order conditions for limitable sequences, $M_{p}$       17
Order conditions for limitable sequences, general      14 27 32
Order of a Hausdorff method      25
Ostrowski's theorem on over-convergence      75
Perfect      18 26
Perfect methods, $C_{\alpha}$       27
Perfect methods, $H^{\alpha}$       29
Perfect methods, $M_{p}$       27
Perfect methods, $N_{p}$       28
Perfect methods, Euler      29
Perfect methods, general      27—32
Perfect methods, Hausdorff      28
Petersen, G.E.      43
Prime number theorem      88
Regular      12
Riemann's zeta function      84—85 100
Riesz      24 63
Riesz methods, $(R,\lambda,\kappa)$       24—26
Riesz methods, $(R^{*},\lambda,\kappa)$       24 26 99—100
RN      11
Schmidt, R.      7
Schnee      47
schur      50
Schur's theorem      13
Slowly decreasing      6 7 80
Slowly increasing      6
Slowly oscillating      5 6 80
Stirling      3
Summability factors      39
Summability functions, $C_{1}$       59
Summability functions, $E_{p}$       60—62
Summability functions, $M_{p}$       60—61
Summability functions, $N_{p}$       61
Summability functions, Abel      62
Summability functions, Borel      62
Summability functions, general      59
Summable      6 15
Szasz      89 95
Tauber      5 7
Tauberian conditions      7 57 59—63 66—68 71 77 82
Tauberian theorems      see also "Tauberian conditions" "Gap-Tauberian
Tauberian theorems, $C_{1}$       6—7 81
Tauberian theorems, $C_{\alpha}$       66 82
Tauberian theorems, $E_{p}$       67
Tauberian theorems, $M_{p}$       46
Tauberian theorems, $N_{p}$       46
Tauberian theorems, (A, $\lambda$ )      69
Tauberian theorems, Abel      67 69—71 81
Tauberian theorems, Borel      68 82
Tauberian theorems, Lambert      83—84
Toeplitz's theorem      11
Translative      45—46
Triangular      14
Vijayaraghavan      69
Wiener      80
Wiener — Levy theorem      98
Wiener's Tauberian theorems      80

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