Bernstein polynomials:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, N.Y.
Chelsea
1986
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 134 S. |
| ISBN: | 0828403236 |
Internformat
MARC
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| 100 | 1 | |a Lorentz, George G. |d 1910-2006 |e Verfasser |0 (DE-588)119043750 |4 aut | |
| 245 | 1 | 0 | |a Bernstein polynomials |c by G. G. Lorentz |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, N.Y. |b Chelsea |c 1986 | |
| 300 | |a X, 134 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Bernstein, Polynômes de |2 ram | |
| 650 | 7 | |a fonction analytique |2 inriac | |
| 650 | 7 | |a formule asymptotique |2 inriac | |
| 650 | 7 | |a méthode Hausdorff |2 inriac | |
| 650 | 7 | |a polynôme Bernstein |2 inriac | |
| 650 | 4 | |a Bernstein polynomials | |
| 650 | 0 | 7 | |a Bernštejn-Polynom |0 (DE-588)4144714-1 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804123649055129600 |
|---|---|
| adam_text | CONTENTS
INTRODUCTION
0.1 Introduction 3
I. BERNSTEIN POLYNOMIALS IN REAL DOMAIN
1.1 The theorem of Weierstrass 5
1.2 Other proofs of the theorem of Weierstrass 7
1.3 Generalizations of the theorem of Weierstrass 9
1.4 Derivatives of the Bernstein polynomials 12
1.5 Estimations and lemmas 13
1.6 The degree of approximation by Bernstein polynomials 19
1.6.1 Asymptotic formulae 22
1.7 Monotone functions, convex functions, and functions
of bounded variation 23
1.8 Further theorems on derivatives 25
1.9 Discontinuous functions 27
II. GENERALIZATIONS OF BERNSTEIN POLYNOMIALS
2.1 Approximation of integrable functions 30
2.2 Approximation of measurable functions 34
2.3 Bernstein polynomials on an unbounded interval 36
2.4 General methods of summation 37
2.5 Euler methods of summation 41
2.6 Degenerate Bernstein polynomials 43
2.7 Divided differences and generalized pn,(x) 44
2.8 Approximation by linear aggregates of functions x° 46
2.9 Some further generalizations 48
ix
x Contents
III. SPACES OF FUNCTIONS AND MOMENT PROBLEMS
3.1 Banach spaces 52
3.2 Functional and moment problems 53
3.3 Moment problems with Stieltjes integrals 57
3.4 Rearrangements of functions 59
3.5 Spaces A and M. Other spaces of integrable functions 65
3.6 Inequalities for spaces A 68
3.7 Continuous linear functionals in spaces A and A* 72
3.7.1 Spaces M( £, p) as conjugate spaces 75
3.8 Moment problems for integrable functions 77
3.9 Hausdorff methods of summation 81
IV. BERNSTEIN POLYNOMIALS OF ANALYTIC FUNCTIONS
4.1 Preliminary theorems 87
4.2 Contour integrals and asymptotic formulae 92
4.3 The loop Lz and its properties 94
4.3.1 Further properties of the loop 100
4.4 The fundamental convergence theorem 104
4.5 Sets of convergence and autonomous sets 107
4.6 Examples of autonomous sets and sets of convergence 110
4.7 Functions analytic on a part of the interval [0, 1] 116
4.8 Summation of power series 117
4.9 Degenerate Bernstein polynomials in the complex domain 121
Bibliography 125
Index 133
|
| any_adam_object | 1 |
| author | Lorentz, George G. 1910-2006 |
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| author_facet | Lorentz, George G. 1910-2006 |
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| callnumber-first | Q - Science |
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| classification_rvk | SK 230 SK 470 |
| ctrlnum | (OCoLC)13430571 (DE-599)BVBBV009208983 |
| dewey-full | 515/.243 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.243 |
| dewey-search | 515/.243 |
| dewey-sort | 3515 3243 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV009208983 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:33:07Z |
| institution | BVB |
| isbn | 0828403236 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006120237 |
| oclc_num | 13430571 |
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| owner | DE-29T DE-573 |
| owner_facet | DE-29T DE-573 |
| physical | X, 134 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Chelsea |
| record_format | marc |
| spelling | Lorentz, George G. 1910-2006 Verfasser (DE-588)119043750 aut Bernstein polynomials by G. G. Lorentz 2. ed. New York, N.Y. Chelsea 1986 X, 134 S. txt rdacontent n rdamedia nc rdacarrier Bernstein, Polynômes de ram fonction analytique inriac formule asymptotique inriac méthode Hausdorff inriac polynôme Bernstein inriac Bernstein polynomials Bernštejn-Polynom (DE-588)4144714-1 gnd rswk-swf Bernštejn-Polynom (DE-588)4144714-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006120237&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lorentz, George G. 1910-2006 Bernstein polynomials Bernstein, Polynômes de ram fonction analytique inriac formule asymptotique inriac méthode Hausdorff inriac polynôme Bernstein inriac Bernstein polynomials Bernštejn-Polynom (DE-588)4144714-1 gnd |
| subject_GND | (DE-588)4144714-1 |
| title | Bernstein polynomials |
| title_auth | Bernstein polynomials |
| title_exact_search | Bernstein polynomials |
| title_full | Bernstein polynomials by G. G. Lorentz |
| title_fullStr | Bernstein polynomials by G. G. Lorentz |
| title_full_unstemmed | Bernstein polynomials by G. G. Lorentz |
| title_short | Bernstein polynomials |
| title_sort | bernstein polynomials |
| topic | Bernstein, Polynômes de ram fonction analytique inriac formule asymptotique inriac méthode Hausdorff inriac polynôme Bernstein inriac Bernstein polynomials Bernštejn-Polynom (DE-588)4144714-1 gnd |
| topic_facet | Bernstein, Polynômes de fonction analytique formule asymptotique méthode Hausdorff polynôme Bernstein Bernstein polynomials Bernštejn-Polynom |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006120237&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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