Constructive function theory: 2 Approximation in mean
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Ungar
1965
|
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 176 S. |
Staff View
MARC
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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 2 |p Approximation in mean |c I. P. Natanson |
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Record in the Search Index
| _version_ | 1804119896654610432 |
|---|---|
| adam_text | CONTENTS
Chapter I. The Space I?p(x)
1. The Problem 7
2. The Weight Function. The Space L2p(x) 9
3. Convergence in Mean 11
4. Classes of Functions Dense in Lp(l) 15
Chapter II. Orthogonal Systems
1. Orthogonality. Examples 19
2. The Fourier Coefficients 23
3. Completeness and Closedness 29
Chapter III. Linearly Independent Systems of Functions
1. Linear Independence. The Gram Determinant.
The Schmidt Theorem 32
2. Approximation by Linearly Independent Functions 36
3. The Muntz Theorems 40
Chapter IV. General Properties of Orthogonal Polynomials
1. Foundations 45
2. Roots of Orthogonal Polynomials. A Recursion Formula 50
3. Relation to the Theory of Continued Fractions 58
4. The Christoffel Darboux Formula. Convergence of
Orthogonal Expansions. 66
5. Changing the Weight Function 74
Chapter V. The Legendre Polynomials
1. The Rodrigues Formula 82
2. The Generating Function 88
3. The Laplace Integral 91
4. Expansions in Terms of Legendre Polynomials 94
CONTENTS
Chapter VI. The Jacobi Polynomials
1. Generalization of the Rodrigues Formula 102
2. The Recursion Formula, Generating Function, and
Differential Equation 107
3. Estimates of the Jacobi Polynomials. The Expansion
Problem. 109
4. Tchebysheff Polynomials of the Second Kind 114
5. The Jacobi Polynomials for a = , 0 = — 121
Chapter VII. The Moment Problem for Finite Intervals
1. Formulation of the Problem 126
2. The Theorems of F. Hausdorff 130
3. Linear Functionals in C and L2 136
4. Positive Definite Sequences 142
Chapter VIII. Infinite Intervals
1. Introduction 147
2. The Laguerre Polynomials 151
3. The Generalized Laguerre Polynomials 153
4. The Hermite Polynomials 156
5. The Moment Problem for Infinite Intervals 159
6. The Favard Theorem 167
Bibliography 171
Index 175
Index of Symbols 176
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| any_adam_object | 1 |
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| author_facet | Natanson, Isidor P. 1906-1964 |
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| author_sort | Natanson, Isidor P. 1906-1964 |
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| id | DE-604.BV005710627 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:33:29Z |
| institution | BVB |
| language | English |
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| physical | 176 S. |
| publishDate | 1965 |
| publishDateSearch | 1965 |
| publishDateSort | 1965 |
| publisher | Ungar |
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| spelling | Natanson, Isidor P. 1906-1964 Verfasser (DE-588)1014768527 aut Constructive function theory 2 Approximation in mean I. P. Natanson New York Ungar 1965 176 S. txt rdacontent n rdamedia nc rdacarrier (DE-604)BV005710625 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003567306&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 2 Approximation in mean I. P. Natanson |
| title_fullStr | Constructive function theory 2 Approximation in mean I. P. Natanson |
| title_full_unstemmed | Constructive function theory 2 Approximation in mean I. P. Natanson |
| title_short | Constructive function theory |
| title_sort | constructive function theory approximation in mean |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003567306&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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