Approximation of functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Chelsea
1986
|
| Edition: | 2. ed. |
| Series: | Chelsea scientific books : numer. mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 188 S. |
| ISBN: | 0828403228 |
Staff View
MARC
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| 245 | 1 | 0 | |a Approximation of functions |c by G. G. Lorentz |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY |b Chelsea |c 1986 | |
| 300 | |a IX, 188 S. | ||
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Record in the Search Index
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| adam_text | Contents
Chapter 1. Possibility of Approximation
1. Basic Notions 1
2. Linear Operators 3
3. Approximation Theorems 7
4. The Theorem of Stone 11
5. Notes 13
Chapter 2. Polynomials of Best Approximation
1. Existence of Polynomials of Best Approximation 16
2. Characterization of Polynomials of Best Approximation 18
3. Applications of Convexity 19
4. Chebyshev Systems 23
5. Uniqueness of Polynomials of Best Approximation 26
6. Chebyshev s Theorem 29
7. Chebyshev Polynomials 30
8. Approximation of Some Complex Functions 32
9. Notes 33
Chapter 3. Properties of Polynomials and Moduli
of Continuity
1. Interpolation 36
2. Inequalities of Bernstein 39
3. The Inequality of Markov 40
4. Growth of Polynomials in the Complex Plane 42
5. Moduli of Continuity 43
6. Moduli of Smoothness 47
7. Classes of Functions 49
8. Notes 52
vii
viii contents
Chapter 4. The Degree of Approximation by Trigonometric
Polynomials
1. Generalities 54
2. The Theorem of Jackson 55
3. The Degree of Approximation of Differentiable Functions 57
4. Inverse Theorems 58
5. Differentiable Functions 61
6. Notes 62
Chapter 5. The Degree of Approximation by Algebraic
Polynomials
1. Preliminaries 65
2. The Approximation Theorems 68
3. Inequalities for the Derivatives of Polynomials 69
4. Inverse Theorems 73
5. Approximation of Analytic Functions 76
6. Notes 78
Chapter 6. Approximation by Rational Functions.
Functions of Several Variables
1. Degree of Rational Approximation 81
2. Inverse Theorems 83
3. Periodic Functions of Several Variables 87
4. Approximation by Algebraic Polynomials 89
5. Notes 90
Chapter 7. Approximation by Linear Polynomial Operators
1. Sums of de la Vallee-Poussin. Positive Operators 92
2. The Principle of Uniform Boundedness 95
3. Operators that Preserve Trigonometric Polynomials 96
4. Trigonometric Saturation Classes 98
5. The Saturation Class of the Bernstein Polynomials 102
6. Notes 108
Chapter 8. Approximation of Classes of Functions
1. Introduction 111
2. Approximation in the Space L1 112
3. The Degree of Approximation of the Classes W* 115
CONTENTS ix
4. Distance Matrices 120
5. Approximation of the Classes Am 122
6. Arbitrary Moduli of Continuity; Approximation
by Operators 124
1. Analytic Functions 126
8. Notes 130
Chapter 9. Widths
1. Definitions and Basic Properties 132
2. Sets of Continuous and Differentiable Functions 133
3. Widths of Balls 137
4. Applications of Theorem 2 139
5. Differential Operators 143
6. Widths of the Sets 9?, 146
7. Notes 148
Chapter 10. Entropy
1. Entropy and Capacity 150
2. Sets of Continuous and Differentiable Functions 153
3. Entropy of Classes of Analytic Functions 155
4. More General Sets of Analytic Functions 161
5. Relations between Entropy and Widths 163
6. Notes 166
Chapter 11. Representation of Functions of Several Variables
by Functions of One Variable
1. The Theorem of Kolmogorov 168
2. The Fundamental Lemma 770
3. The Completion of the Proof 173
4. Functions Not Representable by Superpositions 174
5. Notes 177
Bibliography 179
Index 187
|
| 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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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.4 |
| dewey-search | 511/.4 |
| dewey-sort | 3511 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV006411325 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:45:36Z |
| institution | BVB |
| isbn | 0828403228 |
| language | English |
| lccn | 85072465 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004060271 |
| oclc_num | 13323262 |
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| owner | DE-739 DE-83 |
| owner_facet | DE-739 DE-83 |
| physical | IX, 188 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Chelsea |
| record_format | marc |
| series2 | Chelsea scientific books : numer. mathematics |
| spelling | Lorentz, George G. 1910-2006 Verfasser (DE-588)119043750 aut Approximation of functions by G. G. Lorentz 2. ed. New York, NY Chelsea 1986 IX, 188 S. txt rdacontent n rdamedia nc rdacarrier Chelsea scientific books : numer. mathematics Approximation, Théorie de l' ram Yaklaştırma teorisi approximation complexe inriac approximation réelle inriac entropie inriac épaisseur inriac Approximation theory Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004060271&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lorentz, George G. 1910-2006 Approximation of functions Approximation, Théorie de l' ram Yaklaştırma teorisi approximation complexe inriac approximation réelle inriac entropie inriac épaisseur inriac Approximation theory Approximationstheorie (DE-588)4120913-8 gnd |
| subject_GND | (DE-588)4120913-8 |
| title | Approximation of functions |
| title_auth | Approximation of functions |
| title_exact_search | Approximation of functions |
| title_full | Approximation of functions by G. G. Lorentz |
| title_fullStr | Approximation of functions by G. G. Lorentz |
| title_full_unstemmed | Approximation of functions by G. G. Lorentz |
| title_short | Approximation of functions |
| title_sort | approximation of functions |
| topic | Approximation, Théorie de l' ram Yaklaştırma teorisi approximation complexe inriac approximation réelle inriac entropie inriac épaisseur inriac Approximation theory Approximationstheorie (DE-588)4120913-8 gnd |
| topic_facet | Approximation, Théorie de l' Yaklaştırma teorisi approximation complexe approximation réelle entropie épaisseur Approximation theory Approximationstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004060271&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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