Constructive function theory: 1 Uniform approximation
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Ungar
1964
|
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 232 S. graph. Darst. |
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| 100 | 1 | |a Natanson, Isidor P. |d 1906-1964 |e Verfasser |0 (DE-588)1014768527 |4 aut | |
| 245 | 1 | 0 | |a Constructive function theory |n 1 |p Uniform approximation |c I. P. Natanson |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Introduction vii
Chapter I. Weierstrass Approximation Theorems
1. Weierstrass First Theorem 3
2. Weierstrass Second Approximation Theorem 9
3. The Reciprocal Coherence between the Two Weierstrass
Theorems 16
Chapter II. Algebraic Polynomial of the Best Approximation
1. Fundamental Concepts 20
2. Tchebysheff s Theorems 27
3. Examples. The Tchebysheff Polynomials 34
4. Other Properties of Tchebysheff Polynomials 42
Chapter III. Trigonometric Polynomials of the Best
Approximation
1. The Roots of a Trigonometric Polynomial 57
2. The Image Point Method 59
3. The Trigonometric Polynomial of the Best Approximation 64
4. P. L. Tchebysheff s Theorems 65
5. Examples 72
Chapter IV. Interrelation between Structural Properties
of Functions and the Degree of Their
Approximation by Trigonometric Polynomials
1. Formulation of Problem. Modulus of Continuity;
A Lipschitz Condition 75
2. Lemmata 79
3. D. Jackson s Theorems 84
Chapter V. Characterization of the Structural Properties
of a Function by the Behavior of Its Best
Approximations by Trigonometric Polynomials
1. S. N. Bernstein s Inequality 90
2. Some Elements of Theory of Series 93
3. S. N. Bernstein s Theorems 97
4. A. Zygmund s Theorems 106
vl CONTENTS
5. The Existence of Functions with Preassigned Best Approximation 109
6. Density of Class Hi in Class LipM a 118
Chapter VI. Interrelation between Structural Properties of
Functions and Their Approximation by Algebraic
Polynomials
1. Lemmata 120
2. How the Structural Properties of a Function Affect
Its Approximation 125
3. Converse Theorems 129
4. Bernstein s Second Inequality 133
5. Existence of a Function with Preassigned Approximations 136
6. The Markoff Inequality 137
Chapter VII. Approximation by Means of Fourier Sebies
1. The Fourier Series 141
2. Estimate of the Deviation of Partial Sums of a Fourier Series 149
3. Example of a Continuous Function Not Expandable in a
Fourier Series 153
Chapter VIII. The Sums of Fej^r and de la Valle e Poussin
1. Feje r Sums 157
2. Some Estimates of Fejer Sums 161
3. De la Valle e Poussin s Sums 167
Chapter IX. The Best Approximation to Analytic Functions
1. The Concept of Analytic Functions 172
2. S. N. Bernstein s Theorems on the Best Approximation
to Periodic Analytic Functions 177
3. The Best Approximation to Functions Analytic on a Segment 183
Chapter X. Properties of Some Analytic Expressions
as Means of Approximation
1. Expansion by Tchebysheff Polynomials 195
2. Some Properties of Bernstein s Polynomials 196
3. Some Properties of de la Vallee Poussin 3 Integral 206
4. Bernstein Rogosinsky s Sums 217
5. Convergence Factors 220
Bibliography 227
Index 231
Index of Symbols 232
|
| any_adam_object | 1 |
| author | Natanson, Isidor P. 1906-1964 |
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| bvnumber | BV005710626 |
| ctrlnum | (OCoLC)179746249 (DE-599)BVBBV005710626 |
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| id | DE-604.BV005710626 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:33:29Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003567305 |
| oclc_num | 179746249 |
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| physical | IX, 232 S. graph. Darst. |
| publishDate | 1964 |
| publishDateSearch | 1964 |
| publishDateSort | 1964 |
| publisher | Ungar |
| record_format | marc |
| spelling | Natanson, Isidor P. 1906-1964 Verfasser (DE-588)1014768527 aut Constructive function theory 1 Uniform approximation I. P. Natanson New York Ungar 1964 IX, 232 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier (DE-604)BV005710625 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003567305&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Natanson, Isidor P. 1906-1964 Constructive function theory |
| title | Constructive function theory |
| title_auth | Constructive function theory |
| title_exact_search | Constructive function theory |
| title_full | Constructive function theory 1 Uniform approximation I. P. Natanson |
| title_fullStr | Constructive function theory 1 Uniform approximation I. P. Natanson |
| title_full_unstemmed | Constructive function theory 1 Uniform approximation I. P. Natanson |
| title_short | Constructive function theory |
| title_sort | constructive function theory uniform approximation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003567305&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005710625 |
| work_keys_str_mv | AT natansonisidorp constructivefunctiontheory1 |