Holdings: Bernstein polynomials

Bernstein polynomials:

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Bibliographic Details
Main Author:	Lorentz, George G. 1910-2006 (Author)
Format:	Book
Language:	English
Published:	New York, N.Y. Chelsea 1986
Edition:	2. ed.
Subjects:	Bernstein, Polynômes de fonction analytique formule asymptotique méthode Hausdorff polynôme Bernstein Bernstein polynomials Bernštejn-Polynom
Online Access:	Inhaltsverzeichnis
Physical Description:	X, 134 S.
ISBN:	0828403236

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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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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
open_access_boolean
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
work_keys_str_mv	AT lorentzgeorgeg bernsteinpolynomials

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