Lorentz G.G. — Bernstein Polynomials :: Электронная библиотека попечительского совета мехмата МГУ

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Lorentz G.G. — Bernstein Polynomials

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Название: Bernstein Polynomials

Автор: Lorentz G.G.

Аннотация:

This work gives an exhaustive exposition of the main facts about the Bernstein polynomials and discusses some of their applications in Analysis. The author writes in the Preface to this second edition "After the trigonometric integrals, Bernstein polynomials are the most important and interesting concrete operators on a space of continuous functions. Since the appearance of the first edition of this book [in 1953], the interest in this subject has continued. In an appendix we have summed up a few of the most important papers that have appeared since."

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1986

Количество страниц: 134

Добавлена в каталог: 05.12.2009

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Предметный указатель

"Admissible" lines      100
Absolutely monotone functions      87—88
Almost convergent sequences      38
Autonomous sets      108—114 120—121 123—124
Banach spaces      52—53
Bernstein polynomials      3—6
Bernstein polynomials of analytic functions      87—94 104—117 121—124
Bernstein polynomials of discontinuous functions      27—29
Bernstein polynomials of functions of bounded variation      23—25
Bernstein polynomials on the interval $(0,+\infty)$       36—37
Bernstein polynomials, asymptotic formulae for      22—23 93—94 123
Bernstein polynomials, contour integrals for      92—94 123
Bernstein polynomials, degenerate      43—44 121—124
Bernstein polynomials, degree of approximation by      19—22
Bernstein polynomials, derivatives of      12—13 25—27
Bernstein polynomials, k-dimensional      51
Binomial probabilities $p_{n\nu}(x)$       4
Binomial probabilities $p_{n\nu}(x)$ , estimates for      13—19
Binomial probabilities $p_{n\nu}(x)$ , generalized      45—46
Compact sets      33—34 36
Complete spaces      52
Concave, relatively      68—70
Conjugate spaces      73 76—77
Convex functions      23
Degree of approximation      19—22 48—50
Divided differences      44—45
Dual spaces      76
Equimeasurable functions      see "Rearrangements of functions"
Essential variation      23
Euler methods      41—43
Generalized $p_{n\nu}(x)$       45—46
Generalized Bernstein polynomials      46—48 50—51
Generalized Bernstein polynomials for integrable functions      30—34
Generalized Bernstein polynomials for measurable functions      34—36
Hausdorff methods      81—86
Hoelder, inequality of      31
Inequalities for $\Lambda(\phi,1)$ and $M(\phi,1)$       68 72
Inequalities for $\Lambda(\phi,p)$       71—72
Level functions      70
Linear functionals      53—54 72—73
Linear functionals in space $L^{p}$       57
Linear functionals in space C      55—56
Linear functionals in spaces $\Lambda(\phi,p)$ and $\Lambda^{*}(\phi,p)$       72—74

Linear functionals, positive      56—57
Linear operators      32
Localization, theorems of      7 91—92
Loop $L^{'}_{c}$       109—110 113—114
Loop $L_{z}$       94—104
Measure-preserving transformations      60—61
Method of the steepest descent      106
Methods of summation      37—44 81—86 117—123
Metric means      34
Minkowski, inequality of      31
Modulus of continuity      19
Moment problems      54
Moment problems for spaces $L^{p}$ , M, $\Lambda(\phi,p)$ , $M(\phi,p)$       81
Moment problems for spaces X(C)      77—80
Moment problems for Stieltjes integrals      57—59
Muentz, theorem of      46
Newton's interpolation formula      45
Norm      52 54
Normal spaces      67 72
Perfect spaces      76—77
Polynomials with integral coefficients      6 48—50
probability      4 6 15
Rearrangements of functions      59—61 63—64
Rearrangements of functions, decreasing      60 63
Relation $\prec$       62 70 78
Riesz, inequality of      63—64
Separable spaces      52
Sets of convergence      107—110 114—115 119—123
Space $L^{p}$       31—34 53 81
Space $M(\phi,p)$       65 75—77 81
Space $\Gamma(\phi,p)$       75—77
Space $\Lambda(\alpha,p)$       65—66
Space $\Lambda(\phi,1)$       65 68
Space $\Lambda(\phi,p)$       65 68—75 81
Space C      52—53 55—57
Space S      35—36
Space X(C) (Koethe — Toeplitz)      66—68 79—80
Star-shaped regions      101 118
Stieltjes integrals      54—55
Stone's theorems      9—12
Summability functions      39—41 43 84—86
Summation of power series      117—123
Uniform absolute continuity      79
Weierstrass, theorem of      5—9

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